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TomCo Energy reports near doubling of oil-in-place in Heletz Field
November 24, 2008 by sspillman · Leave a Comment
Tomco Energy announced the results of a revised TRACS (independent reporting agency) report nearly doubling the estimated Heletz Field oil reserves in southern Israel. In addition to the estimated 94.4 million barrels estimated by TRACS (whose report only included the shallow Cretaceous section), Tomco estimates an additional 100 million barrels of reserves at the lower Jurassic level.
Here is Tomco's announcement as reported by the UK's Proactive Investors (http://www.proactiveinvestors.co.uk/companies/news/3549):
TomCo Energy plc (AIM: TOM), the AIM listed oil and gas exploration and production company with investments in the United States and Israel, released an updated independent Reserves and Resource evaluation and audit of the Heletz Field, Israel.
The study, undertaken by TRACS International, ('TRACS') reported an mid-case (P50) estimate original oil-in-place for the Heletz Field of 94.4 million barrels, with a range from 52.7 million barrels (P90) to 164.4 million barrels (P10).
Tomco said the revised estimate represented a "significant increase" over the previously quoted figure of 50 million barrels. The additional resource largely emanated from the inclusion of "substantial additional volumes of oil in lower quality carbonate reservoirs" in the Cretaceous reservoir section of the field.
Around 17 million barrels have been produced from the field to date, mainly from the "better quality sandstone reservoirs" in the middle of the Cretaceous reservoir section.
TRACS International additionally calculated a 2P (Proved plus Probable) reserve of 974,000 barrels, of which 720,000 barrels are Undeveloped Reserves. Tomco and joint venture partner Avenue Energy will be targeting the undeveloped reserves in their 2009 work over and infill drilling campaign. The 3P (Proved plus Probable plus Possible) upside reserves are 1.87 million barrels. Tomco's net interest in these reserves is around 35%.
TRACS further identified 3.5 million barrels of 2C Contingent Resources and 8.5 million barrels of 3C Contingent Resources. Approximately 63% are in the Kokhav Dolomite.
Howard Crosby, the Company's CEO, said: 'We are very pleased with the TRACS Report with original Oil-in-Place (P50) estimates almost double the figure previously released. It is also our belief that the planned work program for 2009 can significantly increase the proven and probable reserves and the Report also confirms the huge up-side potential that further exploitation can unlock at the Heletz Field.'
A Dead Sea Oil Discovery in Jordan?
September 9, 2008 by admin · 2 Comments
Seems like we can't get enough Dead Sea oil discovery news lately. Just today The Jordan Times ran an article apparently confirming the existence of a Dead Sea oil discovery on their side of the salt lake.
According to The Jordan Times:
After years of disappointment, many came to accept that the Kingdom is home to little or no oil reserves.
But with recent claims of the possibility of Jordanian oil, and a parliamentary committee examining the issue, the subject has been elevated to a national discourse steeped in controversy and unanswered questions.
The issue dates back to 1996, when the Natural Resources Authority (NRA) signed a Production Sharing Agreement (PSA) with US company Trans-Global to explore for oil in the Dead Sea area….
Over the next few years, the firm dug four wells at Isaal and Wadi Mujib, some thousands of metres deep, in hope that the rift valley would yield any positive results.
According to the company, logging data and technical studies of the wells revealed huge oil traps of hydrocarbons with significant commercial potential and large oil pays, the solid technical indicators of a major oil discovery.
On August 15, 2005, as per the PSA, the company said it officially informed the NRA of its discovery, but the authority declined to review the studies, according to Trans-Global, which felt there was little interest on the part of the NRA administration to follow through.
"This is the exact opposite of how any petroleum ministry in the world would respond to the discovery of oil," Trans-Global General Manager Nazeeh Abraham told The Jordan Times.
"We claimed a significant oil discovery, and instead of developing it they denied it. We then faced obstructions every step on the way, preventing us from starting a large accelerated drilling development programme," he added.
Frustrated with the lack of interest from the authority, Trans-Global announced the discovery during the 9th International Geological Conference of the Jordanian Geologists Association in Amman in April last year.
The announcement created an uproar and came as a shock to the NRA.
"They went public without ever informing us, which is a breach of the PSA. We were only told of a technical discovery, which doesn't mean much in the oil business," NRA Director Maher Hijazin told The Jordan Times.
"We have all the documents to prove that there is no discovery," he stressed.
Industry experts
Although the announcement was shocking to many, it came as no surprise to Jordanian Geologists Association (JGA) President Khaled Shawabkeh.
He claimed that the NRA drilled at least five wells in the area in the 1990s, and found oil in different quantities, although their commercial viability was not verified.
Lack of support and technical difficulties brought on by the area's topography prevented the authority from any further exploration, and the subject was shelved, he said.
"In my view, Trans-Global has made an oil discovery. The quantity and commercial quality of this discovery should now be explored," the JGA president stressed.
Weatherford, Reeves Logging Ltd., one of 14 third-party companies that performed assessment studies for Trans-Global on the Isaal and Wadi Mujib wells, said it could not confirm or deny the existence of oil in the area, as their only purpose was to log data, not analyse it.
Another industry source, however, told The Jordan Times that the independent third-party studies pointed to "a strong possibility" of commercially viable oil in the Dead Sea area.


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News Section: Opinion
Rick Santorum seems to be positioning himself as the anti-sex candidate. In addition to statements made on women's health issues over the last two weeks, the former Senator from Pennsylvania brings with him a litany of quotes on his personal beliefs and political positions that may play well with the far, far right, though they're likely to have mainstream America scratching its head, should he make it to the big stage, which as implausible as that initially seemed, now appears to be within the realm of some strange reality.
The contraception issue started as just one more red-meat distraction another way to disparage the Affordable Care Act with distortions that could be blasted through chain emails in the same manner as the fictional death panels and exclusive exemptions for Muslims that always seem to proliferate from various obscure websites that have the word liberty in them. But Santorum seized the chance to take the conversation toward arguments he's been making for years long before most Americans were listening.
The absurdity of the issue speaks for itself. The law would have required insurance plans to include several women's health services, including contraception with an exception for churches. The blow up was over Catholic hospitals, universities and other non-church religious organizations that perform secular work, while employing and servicing the public at large. The administration contorted itself into a pretzel to devise something just short of its usual cave-in, ensuring that those services are provided by the insurers directly, and that the religious organizations would not have to pay for them or even fill out paperwork!
Everyone seemed happy. The GOP got to attack President Obama as being not religious enough, while getting some more digs in on the healthcare issue and further confusing Americans as to the President's religion not that it should matter, but he's a lifelong Christian, though polls show that a growing number of Americans are beginning to assume he's Muslim, so obviously the propaganda is working. Only unlike most instances, when it's just the extreme culture warriors who don't leave sleeping dogs lie, the contraception issue didn't dissipate, because the Culture Warrior in Chief, Rick Santorum, is now on a national stage, which is good for far right extremists, bad for moderates, constitutionalists and socially-indifferent fiscal conservatives that want a chance to elect a new president in 2012.
Rick Santorum will never be elected President of the United States and not just because of his track record as a politician which itself should be enough. We're talking about a guy who just a few years back, took the worst Congressional pummeling an incumbent has ever suffered in modern American politics a historic beating, if you will and in a swing state at that. I lived in Pennsylvania when Santorum was in the Senate, and it wasn't the cultural issues that got him trounced it was his record as a Senator, which because of all of these sort of distractions, hasn't received much attention. That's probably good for Santorum who would have a hard time painting himself as a fiscal conservative if it was based on his past performance and not his current talking-point rhetoric.
Today, he's doing surprisingly well in conservative states now that he appears to be the last alternative to Mitt Romney still standing except of course for Ron Paul, who so-called conservatives and even self-labeled Tea Partiers and constitutionalists refuse to get fully behind for some counterintuitive reason. There's also been little attention paid thus far to Santorum's time between Congress and this election, when the beltway insider used his connections to become a multimillionaire Washington consultant, routinely accepting large fees as a media consultant and adviser to many of the causes in his current platform including opposition to healthcare reform. He can play up his coal mining roots in Western Pennsylvania, but the fact is, when Santorum left the Senate, he stayed in Washington as an Audi-driving influence peddler. Yet this guy is marketing himself as the GOP's Washington outsider?
Santorum embodies the far right social-issue wing of the Republican Party, which demands that a pretty long list of blocks are all checked if they're not to boo you off the stage. But consider his positions on sex alone and ask whether you can envision a majority of voters pulling the lever for him. Santorum has been quoted extensively as saying that contraception is not okay, that it is the President's place to step in and warn Americans of "the dangers of birth control," and that such policies should reflect the notion that sex is only to be engaged in by married couples and even then, only for the purpose of procreation. We're not talking sound bites and gotcha politics. This guy we'll say that to anyone who puts a microphone in front of him.
99 percent of women use birth control during their lifetime slightly less than the number who have sex. Many use it for reasons other than sex, like endometriosis to name just one. Others use it for family planning, like when they decide that they couldn't responsibly afford to properly raise another child. Others still, use it to avoid unwanted pregnancies that lead to the other holy grail of social issues abortion. I know I'm not the first person to point out that reducing access to birth control and reducing abortions seem mutually exclusive in any practical sense.
Santorum has arguably done more for the sweater vest
than anyone since Cliff Huxtable.
Photo by Gage Skidmore via Wikimedia
Even the Catholic Church caved on the sex for procreation issue and that was all the way back in 1930! The church has condoned Natural Family Planning methods such as timing the menstrual cycle (the infamous rhythm method), ostensibly because the infertile period was created by God, but just as likely because it became pretty clear that human beings have sex whether you tell them to or not.
Then there's the homosexuality issue. At an earlier Fox News debate, Santorum got his first bit of national spotlight for famously piling on the gay Iraqi war-veteran soldier who asked about candidates' policies toward gays in the military and was booed mercilessly, by saying that not only does he oppose homosexuals being able to serve openly, but that any type of sexual activity has absolutely no place in the military.
If that's the policy, we really will have an Army of one assuming we can find a young healthy American male (Santorum doesn't believe in women serving in combat either) not only willing to risk his life in whatever Middle Eastern desert someone like Santorum sends him to, but do so while celibate, at least as long as he's in the military. Afterward, he could seemingly come home, and assuming he gets married and he and his wife want to have a child, engage in coitus a few times, at least until they're done procreating. What if one's sterile; are they out of luck? I'm not sure anyone's asked Rick that one yet.
I'm not looking for a culture war here, and in truth, as disturbed as I think the guy in the sweater vest is, I admire the fact that he wears his crazy on his sleeve where voters can see it. It doesn't matter where you stand on the issue of sex. Personally, I'm in favor of it and I think it's pretty clear I'm with the vast majority of Americans, at least on this one. What I am suggesting is that someone with such radical views is pretty much disqualified in terms of getting elected. If this is all you've got, it's Romney or it's Obama deal with it.
The biggest demographic challenge President Obama faces is a disenchanted youth vote, whose record turnout was the biggest factor in his 2008 victory. While unlikely to vote for any of the Republican candidates (again with the exception of Congressman Paul who polls very well with those under 30 across the spectrum), they might not turn out for a president who has largely been a disappointment to them on touchstone issues like the environment and foreign policy. But put Santorum on the ticket, and I can think of no better way to galvanize young voters and spike turnout for the President.
I don't know how many lukewarm young voters will come out to vote against Mitt Romney, but I suspect they'd be tripping over themselves to turn out to vote against the guy who has denied the science of global warming (he calls it a "hoax"), doesn't think abortion should be legal even in cases of rape and incest, advocates discriminating against homosexuals at every turn (he's even lumped it in with bestiality and incest), has promised to invade Iran, denies the very existance of Palestinians (because there is no Palestine), doesn't think birth control should even be used in the first place, let alone covered by insurance, because Americans are only to have sex for the purpose of procreation, etc., etc. Yea, good luck with that.
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subset: commoncrawl


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Tony Tyler's address to the 1000 delegates from industry and media who gathered in Miami 7-9 June for IATA's 71st AGM
Press Release No.:
Date: 6 June 2006
(Paris) The International Air Transport Association (IATA) honoured two governments—Chile and Egypt—for their leadership in promoting safety by incorporating the IATA Operational Safety Audit (IOSA) into their safety oversight programmes. Moreover, the association's 261 members, representing 94% of scheduled international traffic, commended the Arab Civil Aviation Commission (ACAC) for the resolution passed at its recent General Assembly urging its sixteen member states to require IOSA registration for any carrier based in their territories or using their airports.
The IATA Annual General Meeting also formally approved a resolution requiring that all IATA members be IOSA registered. All new members of the association will be required to pass IOSA before they join. And all existing members must contract for an IOSA audit by the end of 2006 and complete an audit by the end of 2007 to retain membership.
"We are serious about safety," said Giovanni Bisignani, IATA's Director General and CEO. "IATA is a quality association and we have set the bar high to ensure that our membership represents best practice in safety. At the same time we are encouraged that governments not only understand the benefits of IOSA, but also are using it. I encourage more governments to use this great tool."
IOSA was launched in 2003 as the industry's first global standard for airline safety management. Fully 189 member airlines and 57 non-members are now in the IOSA process, representing over 80% of scheduled international traffic. IOSA registration lasts for two years, at which time a recurrent audit is required to ensure ongoing compliance with IATA standards.
IOSA standards are based on International Civil Aviation Organisation (ICAO) standards and industry best practice and are freely available to any commercial airline as part of IATA's commitment to safety. For airlines with limited resources, IATA's Partnership for Safety programme is helping to bridge the gap. The scope of Partnership for Safety expanded from Africa to include Latin America. In both regions, the number of accidents is disproportionately large when compared with traffic volumes.
"Safety is our number one priority. Last year was the air transport industry's best year ever with an accident rate of 0.76 per million sectors—one accident for every 1.3 million flights. IATA members did considerably better at 0.35 per million sectors - one accident for every 2.9 million flights. Governments increasingly accept the IOSA standard. And we will do our utmost to ensure that all IATA members are on board by the deadlines. But after the deadline, we cannot accept any exceptions. Safety is just too important," said Bisignani.
· First global standard for airline operational safety auditing launched in 2003
· The programme is designed to assess the operational management and control systems of an airline.
· It improves safety throughout the airline industry as well as helping airlines share audit resources and reduce the overall number of audits performed.
· Audit standards were developed in cooperation with regulatory bodies including the US Federal Aviation Administration (FAA), Australia's Civil Aviation Safety Authority, Transport Canada, and Europe's Joint Aviation Authority.
· IATA oversees the accreditation of audit and training organisations, ensures continuous development of IOSA standards and recommended practices, and manages the central database.
· Currently 102 airlines (including 89 IATA members) are on the IATA Registry, which is publicly available at www.iata.org/registry.
© International Air Transport Association (IATA) 2015. All rights reserved.


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Biodiversity information
is biodiversity?
What is taxonomy?
What is systematics?
The mention of biodiversity commonly conjures up images of steaming tropical forests, and these are without doubt some of the most diverse areas on the planet. But did you know that the UK is also an area rich in biodiversity?
Biodiversity comes from the words 'biological diversity'. In its simplest sense it refers to all the life forms on Earth. You can find biodiversity all around you - it is all the plants, animals, fungi and micro-organisms, the differences within and between species, and the communities which they form.
Taxonomy is the science of naming and classifying fossil and living organisms. A classification system provides a way of organizing knowledge about the natural world. It helps to make sense of the enormous diversity of life. The best-known system was invented by Linnaeus in the eighteenth century. Including the Latin 'binomial' (genus and species) it remains the basis of many modern methods.
Systematic biology includes taxonomy. It is the science in which we discover, describe, name and classify living and fossil organisms,
and work out their evolutionary relationships. Find out more in Web of Life, from the UK Systematics Forum.
taxonomy to give shape to the bricks, and systematics to tell us how to
put them together, the house of biological science is
a meaningless jumble.'
Robert May
Chief Scientific Advisor
to the Government


text:
In a method for generalizing the conventional Viterbi algorithm, in which the transition costs are formed in a metric increment unit (TMU) and adding, comparing and selection are performed in a succeeding add-compare-select (ACS) unit, the difference costs from two arriving paths are calculated for each individual state, the reliability information at the beginning of each path being set to the highest value. Then the reliability value of the path with the least costs is updated at the points where the information points differ from the competing path, updating being performed in accordance with a table, and where the prior value of the reliability information and the difference costs are inserted into the table as the new input values. Then this new value is taken from the table and is stored, together with hard decisions, as path memory, where storage can be in the form of fixed or floating point values. Finally the analog value decision is read out from the point which, after a decision delay, is the result for the path with the lowest cost and where the hard decisions of the conventional Viterbi algorithm are the sign of the analog value decision. By means of the method according to the invention a Viterbi algorithm has been created at the output of which analog value decisions, i.e. soft decisions are supplied.
1. A method for generalizing a conventional Viterbi algorithm in which transition costs are formed in a transition metric unit (TMU) and adding, comparing and selection are performed in a succeeding add-compare-select unit (ACS), comprising the steps of
calculating different costs from two arriving paths for each individual state;
setting a reliability information at the beginning of each path at a highest value;
updating a reliability value of the path with least costs where information points differ from a competing path by performing said updating in accordance with a table;
feeding a prior value of the reliability information and difference costs ( ) into the table as input values:
taking the said input values from the table and storing said values along with hard decisions, as path memory, in the form of fixed or floating point values;
reading out an analog value decision from a point which, after a defined decision delay (δ) is the result for the path with the lowest cost;
said hard decisions of the conventional Viterbi algorithm being signs of an analog value decision.
2. The method for modifying the Viterbi algorithm in accordance with claim 1 further comprising
forming normalized path difference costs (Δ/α) for updating the reliability information from a minimum from an old reliability information including
introducing a factor (α);
and storing a new value so derived as path memory.
3. The method for modifying the Viterbi algorithm in accordance with claim 1 further comprising
checking information bits of two competing paths for concurrence within a defined area (k-v to k-δp with v≦δp ≦δm) to accomplish path updating with a path updating unit (PAU);
and activating an updating procedure if a non-concurrence is noted
where k identifies a time index, v, a code memory and δ, a decision delay.
4. A device for generalizing a conventional Viterbi algorithm comprising
a metric increment unit (TMU) in which costs are formed;
an add-compare-select unit (ACS) in which addition, comparison and selection are performed;
two competing paths;
a path RAM and a path updating unit (PAU) placed after said add-compare-select unit (ACS) and after said two competing paths to check information bits of said two competing paths in time interval k-v to k-δm for concurrence, and in case of non-concurrence to activate the updating process in the path RAM.
5. The device in accordance with claim 4 further comprising
a means for normalizing the updating of reliability information by introducing a factor α to satisfy a fixed point representation and to avoid overflow.
6. The device in accordance with claim 4 further comprising
a parallel arrangement of each said path updating unit (PAU) for each S state provided so that on the basis of parallel arrangement in view of providing only a single path updating unit (PAU), a gain in time of the value of a factor S is achieved.
7. The device in accordance with claim 4 further comprising
a separate said path updating unit (PAU) for each time interval k-v to k-δp providing a parallel arrangement so that because of said parallel arrangement gains of the value of a factor (v-δp) are attained.
1. Field of the Invention
The invention relates to a method for generalizing the Viterbi algorithm and devices for executing the method. The Viterbi algorithm described by G. D. Forney in Proc. of the IEEE, vol. 61, No. 3, pp. 268 to 278, March 1973, has become a standard tool in communications receivers, by means of which various functions, such as demodulation, decoding, equalization, etc. are performed. In an increasing number of applications two Viterbi algorithms are being used in a concatenated way. Examples of this are coded modulation systems without bandwidth expansion, such as coded QAM (quadrature amplitude modulation) together with CPM (continuous phase modulation), in which Viterbi receivers replace classical modulation methods. With an additional outer coding system convolutional codes with Viterbi coding can be used in order to perform FEC (forward error correction) decoding. However, such a solution has two drawbacks: for one, the inner Viterbi algorithm creates bursts of errors during demodulation, to which the outer Viterbi algorithm is very sensitive, and for another, the inner Viterbi algorithm creates hard, i.e. binary decisions, so that the capability of the outer Viterbi algorithm to produce so-called soft decisions, i.e. analog decisions, cannot be utilized. The first drawback can be compensated by means of interleaving between the inner and outer Viterbi algorithms. In the second case soft decisions, i.e. reliability information together with the decisions of the inner Viterbi algorithms are desirable. This would improve the effectiveness of the outer Viterbi algorithm considerably.
Similar problems arise if convolutional codes for FEC coding are used in channels requiring equalization. This is the case, for example, in the proposed pan-European Mobile Radio System (GSM). In this case a Viterbi equalizer produces only hard decisions which result in a reduced performance of the outer Viterbi algorithm in which FEC decoding is performed.
A further possibility rests in the use of a Viterbi algorithm for decoding blocked or terminated convolutional codes. This is a convolutional code with memory ν, terminated by υknown symbols. Often a source decoder requires reliability information regarding the correct coding of the entire frame or of parts which can be used for concealing or interpolation of the source signals. Up to now, when an inner Viterbi algorithm was used, the correct choice for the outer code was considered to be a Reed-Solomon (RS) code for its burst correction capability, because by means of this RS code the residual errors of the Viterbi algorithm could be reduced. However, the full capabilities of an RS decoder can only be realized if error and erasure decoding is used. The desired ML (maximum likelihood) decoding of RS codes is not yet available at this time. But erasure as well as RS decoding would require soft decisions of the first Viterbi algorithm which, at a certain threshold value become erasures. Even simple block codes, such as parity check codes, could be decoded much better with the aid of soft decisions.
The Viterbi algorithm was introduced in 1967 as a method for decoding convolutional codes (see A. J. Viterbi, IEEE Trans. Inform. Theory, Vol. IT-13, pp. 260-269, April 1967), and shortly thereafter it was possible to show that the algorithm was optimal in the ML (maximum likelihood) sense (see, for example, I. K. Okura in IEEE Trans. Inform. Theory, Vol. II-15, pp. 177-179, Jan. 1969).
2. The Prior Art
Attempts to reduce the bit error probability to channels with intersymbol interference lead to a receiver structure which is less attractive than the Viterbi algorithm. This algorithm therefore was generalized (see, for example, L. R. Bahl et al, IEEE Trans. Inform. Theory, Vol. IT-20, pp. 284-287, March 1974). It was shown that the algorithm is optimal in the sense of a MAP decision and provides for each bit the corresponding a-posteriori probability (APP). However, because of the greater complexity the number of applications is limited.
Numerous further attempts were made for deriving reliability information. However, no proposal is known to applicant in which the a-posteriori probabilities (APP) of the MAP detector or a soft decision are used on the basis of an augmented Viterbi algorithm in order to perform optimal outer soft decision decoding.
Although soft decisions are accepted by a Viterbi receiver, it only supplies hard decisions. The next receiver stage, however, would work better in many cases if soft decisions, i.e. analog values, could be derived for each symbol. However, there is no direct way to extract soft decisions for each individual symbol in the conventional Viterbi algorithm.
It is therefore an object of the invention to develop a method and a device for generalizing a Viterbi algorithm in such a way that the Viterbi algorithm produces analog, i.e. soft decisions.
In accordance with the invention, in a method for generalizing the conventional Viterbi algorithm, in which the costs are formed in a transition metric unit (TMU) and adding, comparing and selection are performed in a succeeding add-compare-select (ACS) unit, the difference costs from two arriving paths are calculated for each individual state, the reliability information at the beginning of each path being set to the highest value. Then the reliability value of the path with the least costs is updated at the points where the information points differ from the competing path; updating is performed in accordance with a table, in which the prior value of the reliability information and the difference costs are arranged in the table as the new input values. This new value is then taken from the table and is stored, together with hard decisions, in the form of a so-called path memory; storage can be in the form of fixed or floating point values. Finally an analog value decision is read out from the point which, after a defined decision delay, is the result for the path with the lowest cost. The hard decisions of the conventional Viterbi algorithm are the signs of the analog value decision. In the method for a modification of the method of the invention for generalizing the Viterbi algorithm, the minimum from the old reliability information and--by the introduction of a factor α--normalized path difference costs is formed for updating the reliability information, and this new value is then stored as path memory.
In accordance with a preferred improvement of the method for generalizing or modifying the Viterbi algorithm, a path update unit is provided for path updating, by means of which in a defined area (k-ν to k-δp with ν≦δp ≦δm) the information bits of the two competing paths are checked for concurrence and, if non-concurrence is noted, the updating procedure is activated; in this connection k identifies a time index, ν a code memory and δ a dicinon delay.
In a preferred device for executing the method, there are provided, besides the known units required for executing the Viterbi algorithm, namely a metric increment unit (TMU) and an add-compare-select unit, additionally a path RAM as well as a path updating unit (PAU), where for path updating in an exactly defined area, namely in the area k-ν to k-δm, the information bits of the two competing paths are checked for concurrence and, in case of non-concurrence, the updating process in the path RAM is activated.
In accordance with an advantageous improvement of the device of the invention, a device for nonstandardizing the updating of the reliability information is provided, where a factor (α) is introduced, which makes a fixed point representation possible and avoids overflow at the same time. If it is desired or required to gain time, a separate path updating unit (PAU) is provided for each one of S states, where, on the basis of this parallel arrangement in view of the provision of only a single path updating unit (PAU), a gain in time of the value of the factor S is achieved.
It is also possible in accordance with a further advantageous design to provide for each time interval (k-ν to k-δp) a separate path updating unit (PAU) where it is possible, because of this parallel design, to attain gains in time of the value of a factor, namely ν-δp, where ν again is the code memory and δp a dicinon delay.
Thus, by means of the present invention a conventional Viterbi receiver is augmented by a so-called soft deciding device, i.e. a device delivering analog decisions, i.e. soft decisions, which are always better than hard, i.e. binary decisions. However, the extent of what can be- gained by this depends on the manner in which the next receiver stage operates. Minimally a value of 2 dB is attainable symptomatically, while the maximum gain may lie at more than 10 dB. Such a gain is impossible to attain in a classic Viterbi receiver.
The Viterbi algorithm (VA) with analog value decision (SD) can be used in all areas in which conventional Viterbi algorithms can also be used, namely as a decoder, an equalizer or a demodulator for coded modulation. In all these cases it is only required to exchange the metric increment unit, i.e. the so-called TMU, in a known manner. The same is true for applications for punctured codes or in use as a demodulator with reduced status number.
Therefore, in accordance with the invention it is possible to use MAP (maximum a posterior) or a Viterbi detector in a receiver chain. This could be a Viterbi equalizer, a Viterbi demodulator (for example for modulation processes of constant envelopes (CPM) or for trellis-coded modulation (TCM)), or a Viterbi decoder for an inner convolutional code. A second detector follows this device which could be a demodulator or decoder following the equalizer, a decoder following the demodulator, an outer decoder following an inner decoder, or a source decoder. The performance of the second device is improved in that, besides binary decisions, i.e. hard decisions, reliability information or analog value decisions, i.e. soft decisions, are available from the first stage.
It is further possible by means of the invention to improve all previously mentioned possibilities of use as well as other uses, such as adaptive Viterbi schemes; FEC (Forward Error Correction)/ARQ (Automatic Repeat Request) schemes, a Viterbi synchronization with the aid of the Viterbi algorithm (VA) in accordance with the invention with analog-value decision (SD) that is with the aid of a Soft Deciding Viterbi Algorithm (SDVA). This is a Viterbi algorithm which uses soft (or hard) decisions for calculating metrics, but also decides soft, i.e. analog, and thus not in a hard, i.e. binary form. A particularly advantageous way consists in providing, together with the decisions, reliability information, i.e. the probability of a correct decision or a logarithmic probability function.
The optimal way consists in calculating a-posteriori probabilities (APP) for the decision and to form an algorithm for making Maximum A-Posteriori (MAP) decisions. The SDV algorithm in accordance with the invention thus is completely different from the Viterbi algorithm, although it is only required to provide the latter with a small additional device in the form of a unit supplying analog value decisions, a so-called soft deciding unit.
The invention will be described in detail below by means of preferred embodiments.
FIG. 1 is a block diagram of a detector for a Viterbi algorithm with analog value decisions and with reliability information in accordance with the invention;
FIG. 2 is an example of a Viterbi algorithm with analog value decisions (SDVA);
FIG. 3 is a block diagram of a Viterbi algorithm with analog value decision (SDVA) with a so-called pipelining effect;
FIG. 4 is a block diagram of a path RAM and a metric RAM;
FIG. 5 is a schematic of a updating operation or an updating of an analog value decision (SD);
FIG. 6 is a schematic view of a path updating unit (PAU) in accordance with the invention.
In FIG. 1 a Viterbi detector of the first stage, by means of which a Viterbi algorithm with analog value decisions is performed, provides estimates u for the symbol sequence u' by processing the received symbol sequence y in a MAP or Viterbi detector. In the course of this the detector is to provide reliability information for each symbol, i.e. an estimated value for the probability that this symbol has been incorrectly detected:
pk ' =Prob{uk ' ≠uk ' |y}(1)
This estimated value u' is not always correct. Therefore a conditional probability density function p(p'k p'k) is provided, which describes the estimate error for estimating p'k, given by p'k. Since the Viterbi algorithm of the first stage generates correlated errors in u'k and p'k, which could degrade the performance of the next stage, sufficient interleaving is applied to attain statistical independence (the primes have been dropped). This, of course, requires a suitable interleaving device at the transmitter.
At the dashed line A--A' of FIG. 1 the detector of the first stage supplies symbols uk with statistically independent error probabilities pk. Such a channel is called a discrete, memory-free compound channel, which supplies an estimated value pk for these error probabilities pk. If the error probability density p(pk) and the estimate density p(pk pk) are given, the channel capacity of such a compound channel can be calculated. For binary values uk, such a channel can be considered a binary, symmetrical channel (BSC) with an error probability pk, which changes from bit to bit by a statistically independent value pk in accordance with the density function p(pk). This error probability can be assigned a probability of p(pk pk).
For a detector of the second stage the channel is a discrete (binary), memory-free compound channel with output pair values (uk, pk). If the detector of the second page performs an ML (maximum likelihood) detection, the optimal ML metric is ##EQU1## where xk.sup.(m) =�1 is the k-th symbol of the m-th information sequence. The value uk is the hard decision (�1) of the first Viterbi detector. Since this hard decision is to be weighed with log (1-pk, uk log (1-pk)/pk can be considered to be a soft decision variable. Accordingly, the first Viterbi algorithm is called a soft deciding Viterbi (SDV) algorithm, because it supplies soft decisions ##EQU2## which must be processed by the next ML detector stage. The detector of the next stage again may be a Viterbi algorithm which accepts soft decisions and finally supplies hard decisions. Usefully it again may be a soft deciding Viterbi (SDV) algorithm, which provides reliability information together with the decisions, which could be used in a decoder of the next stage or the source decoder. In the same way the soft decisions according to (3) could be quantized into three values (-1, 0, �1), which therefore indicate errors and erasures, which are usable in case the detector of the second stage is an RS or other block decoder. The Viterbi algorithm (VA) must then be modified so that it becomes a soft deciding Viterbi (SDV) algorithm supplying soft decisions (3) with pk, which has been approximated as closely as possible to pk. Two solutions are being investigated below:
In the first solution a device generates decisions having an optimal value of pl =pk, or an optimal value for log(1-pk) pk =log(1-pk)/pk. This is the known "maximum" a-posteriori (MAP) algorithm, which includes an estimated value for pk. This algorithm, here designated as soft deciding MAP(SDMAP) algorithm differs from the Viterbi algorithm and is more complex. The first solution is not a subject of the present method, it is only used as a reference.
The second solution is the SDV algorithm, of which it is required that it supplies the same hard decisions as the Viterbi algorithm, which are only ML for the sequence and not MAP for the symbols. Therefore the original Viterbi algorithm is used and is expanded by an error probability evaluation device which in the end provides the value uk log(1-pk)/pk for each bit uk as the soft decision value. In this connection the additional complexity should be kept as small as possible. Furthermore, soft decisions should be provided at the same time k at which the decision of uk is available in order to avoid further delays.
Regarding the receiver, for simplicity's sake there is a limitation to trellis diagrams with two branches ending at each node point. For trellis diagrams with more than two paths per state, in an optimal way it is required to compare the survivor path with each other path in succession. This reduces the search to the binary case and the method takes place as described. A more economical method consists in comparing the survivor path only with the p next-best paths, in the extreme case only with the second best path, where p then equals 1.
In a conventional convolutional code of the rate 1/N, exactly N channel bits are transferred for each arriving information bit; if not all information bits are transferred, but suitable channel bits are erased or "punctured", the result is a code with the rate K/N. The code rate can thus be increased. The advantage of the punctured codes lies in that the trellis diagram remains the same in principle, in particular the number of paths remains unchanged. This does not change the coding effort. This includes punctured codes of the rate K/N deriving from a code of the rate 1/N, because they use the net diagram of the code with the rate 1/N.
The number of the states S of the decoder is S=2ν, where ν is the code memory; however, decoders with a reduced number of states are also possible.
The classic Viterbi algorithm makes a final decision with a delay δ, where ν is sufficiently large so that all 2ν-survivor paths have joined with a sufficiently large probability. As shown in FIG. 2, the Viterbi algorithm has one survivor path each for the state sk at the time k, where 1≦sk ≦S=2ν. This is accomplished by selecting the path with the maximal probability metric, which for the Gaussian channel is the logarithm of the Gaussian probability density, ##EQU3## where x.sup.(m)jn is the n-th bit of N bits in the branch for the m-th path at the time j, Yjn is the received value at the same position, and Es /N0 is the signal-to-noise ratio (SNR). By means of this formula the result is if the path with the higher metric is designated as m=1. Then this means M1 ≦m2, which in turn includes that the Viterbi algorithms selects the path 1. The probability that the wrong survivor path will be selected then is: ##EQU4##
The value of psk is 0.5, if M1 ≈M2, and approaches 0, if M1 >M2. With this probability psk the Viterbi algorithm has made errors at all the e-positions where the information bits of path 2 differ from path 1. By e-position that number of positions is indicated where the information bits of the two investigated paths differ from one another. For example, in FIG. 2 the information bits differ in the interval from k-4 to k-3 and in the interval from k-3 to k-2. In all other time periods the bits are equal in pairs. Thus, in this example e=2.
uj.sup.(1) ≠uj.sup.(2), j=j1, . . . , je(7)
Positions where uj.sup.(1) =uj.sup.(2) are not affected. Let the value δm be the length of these two paths until they meet. The result then is e different information values and (εm -e) non-different values. If then the probabilities pj of prior erroneous decisions at the path 1 have been stored, then these probabilities for the e differing decisions on this path will be updated corresponding to
Pj =Pj (1-pek)+(1-pj)pek, j=j1, . . . , je, 0≦pj ≦0.5 (8)
To do this, the information bits of the two paths must be compared with each other to determine the places where they differ. However, in this connection it should be noted that the first ν bits are equal, because the two paths end in the same bit state. An indicator δp can be stored for all states to show the maximal length of paths that have not merged and to search only from j=k-ν to j=k-δp. Also, the recursion could be performed directly in accordance with the ratio of probability: ##EQU5## By means of equations (6), (8) and (9) and after appropriate conversion, the following is the result: ##EQU6## The function f(Lj, Δ) should be tabulated with Lj, and Δ as input variables and need not be calculated for each step. The factor α prevents overflow in case of a large signal-to-noise ratio. The factor α is correctly chosen as ##EQU7## where dfree is the free distance of the code. The function can also be approximated by
f(Lj, Δ)=min (Lj, Δ/α). (11a)
It is now possible to formulate the soft deciding Viterbi (SDV) algorithm:
______________________________________Storage:k (time index, modulo δ + 1)u(sk) = {uk-δ (sk), . . . , uk (sk)}, 1 ≦ sk ≦ S (hard decision values, u ε {�1})L(sk) = {Lk-δ (sk), . . . , Lk (sk)}, 1 ≦ sk ≦ S (reliability values, - soft decisions, 0 ≦ L ≦ ∞)Γ(sk), 1 ≦ sk ≦ S (accumulated metric values = survivor cost)Initialization:u(sk) = 0, 1 ≦ sk ≦ SL(sk) = +∞, 1 ≦ sk ≦ S (*)Γ(s0) = 0, Γ(i) = +∞, i ≠ s0.Recursion:a) Classical Viterbi step:For each state skCompute ##STR1##for both transitions (sk-1, sk).Find Γ(sk) = min Γ(sk-1, sk).Store Γ(sk) and the corresponding survivor uk (sk).b) Soft-deciding update: (*)For each state skCompute Δ = max Γ(sk-1, sk) - minΓ(sk-1, sk).Initialize Lk (sk) = +∞.For j = k - v to j = k - δmCompare the two pathes merging in skif uj.sup.(1) (sj) ≠ uj.sup.(2) (sj) thenupdate Lj := f(--L j, Δ)c) Final decision:Find state sk opt with min Γ(sk).The hard decision is uk-δ (sk opt) ε {�1}.The soft decision is uk-δ (sk opt) �Lk-δ (sk opt) ε R. (*)d) Set k to k + 1 |mod δ+1 and repeat.______________________________________
The classical Viterbi algorithm in accordance with the invention has only been augmented by the steps marked by (*). For improved definition of the algorithm the hard and soft decision values are stored in two different fields of the length δ+1 (see FIG. 4). In this connection the hard decision values can be considered to be the signs of the soft decision values. Storage is performed modulo δ+1 in order to allow messages of optional length. Of course it is also possible to make the final decision first and then the free position can be overwritten with the actual values. This means a modulo δ operation and leads to a reduction in respect to the memory size. Initialization with +∞ indicates the highest possible value.
Additive metrics have the property that a multiplication or addition not depending on y does not change the decision. This makes it possible to update ##EQU8## Since it is true that xkn ε{+1}, a real value multiplication can be avoided. Furthermore, it is possible to drop the factor 2 Es /N0 and to account for this term in the calculation of Δ either by multiplication or expansion of the actual table to the form f(Lk, Δ, Es /N0). A signal-to-noise ratio must be calculated with the help of known methods. However, a poor guess has only a negligible effect on the performance and does not affect the sign of the decisions.
In place of the optimal procedure as described above, two modified solutions requiring less effort are offered:
1. The state with the most advantageous metric is determined and only the ML path is updated. This results in a reduction of the soft updating by a factor of S.
2. The search generally is only performed in the range where j=k-ν to j=k-δ', with δ'<δm ≦δ. In connection with 2. it must be emphasized that the information bits in the interval k-(ν+1) to k-ν always differ. Therefore a solution would be to put δ'=ν+1. This special case is interesting because a "search" need not be performed and because the so-called "update" value is replaced by a one-time operation. It is possible to write Δ=M1 -M2 directly as reliable value to the associated memory position of the path surviving each state. Initialization is therefore useless. Finally, it should be noted that the classical Viterbi recursion can be nonstandardized with the help of the standard solutions. The latest soft deciding values, with the exception of the value α, do not require further nonstandardization.
As schematically indicated in FIG. 4, with an ns soft bit decision and fixed point arithmetic, each survivor path of the length δ comprises ns �δ bits. The first one of the ns bits is the sign bit or the hard decision bit. The probability values then are Lk ε{0.1 . . . , 2ns-1 -1}. Lk =0 indicates the most unreliable value and Lk =2ns-1 -1 indicates the most reliable value. If the metric difference Δ is given, which has been quantized with n.sub.Δ bits, the updated probability value is shown in the table illustrated in FIG. 6. The table is calculated only once with the aid of equation (10) and is then stored in the ROM memory. Accordingly, the additional effort of the soft deciding Viterbi (SDV) algorithm in comparison to the Viterbi algorithm is:
2.sup.ν �δ�ns bits instead of 2.sup.ν �δ bits
Reference table with 2nΔ+ns-1 vectors with ns -1 bits each.
Computation Effort:
Maximally 2.sup.ν �(δ-ν) bit comparisons
2.sup.ν �e table references to update Lk
Long-term channel estimate value for computing the signal-to-noise ratio.
The data transfer will be explained in detail below.
The value e is a random number and is dependent on the channel noise and the code structure. The following is applicable for a high signal-to-noise ratio: ##EQU9## where cdfree is the total number of bit errors in all adfree paths with free distance ddfree, nonstandardized to one information bit. For a lower signal-to-noise ratio, the value e is upwardly limited by
1/2(δ-ν) (14)
The soft deciding Viterbi (SDV) algorithm can be performed in a "pipeline" structure (clocked at a symbol rate of 1/T) (see FIG. 3)). Accordingly, very high speed implementation is possible. The units required for this are a metric increment unit (transition metric unit (TMU)), an add-compare-select (ACS) unit and a path RAM (including a path updating unit (PAU)). There is no interaction between the ACS unit and the path memory RAM.
For each symbol yk received the TMU unit calculates the metric increments for all possible transitions. This unit is the same as the corresponding unit in a conventional Viterbi algorithm. If the (soft deciding) Viterbi algorithms operates as demodulator, decoder or equalizer, only another TMU unit need be added.
The TMU unit provides the metric increments to the ACS unit which performs the metric updating (see equation (12)). The ACS unit, too, remains unchanged in comparison with the conventional Viterbi algorithm. The ACS unit is the bottleneck in Viterbi algorithms. This units limits the speed because each recursion must be terminated before the next one can start. Further pipelining of this unit is impossible. Accordingly, for time-critical operations this unit is provided in parallel form for each state. The only modification of the ACS unit for the soft deciding Viterbi algorithm is made for calculation of Δ, and is only an n-bit subtraction and for the increased data transfer between the ACS unit and the path storage unit of (1+n.sub.Δ) bits instead of one bit.
Finally, the data are stored in the path RAM; therefore only this memory device needs to be changed. Normally, information is decoded in every state and the information bit(s) is (are) stored in that sequence which had been the result in the previous state. Now not only the hard information bits, but also a vector of ns bits also containing the reliability information is stored.
A block diagram of a modified path RAM is shown in FIG. 4. It is arranged as a 2.sup.ν �δ�ns matrix, where 2.sup.ν �δ� bits are assigned to the hard decision while the rest is reliability information.
The soft decision updating is shown in FIG. 5. Two paths are assumed, which diverge at the time k and merge at the time k-δm (see FIGS. 2 and 4). A so-called path updating unit (PAU) is used and "slides" over the stored information bits. The range where the information bits u.sup.(1) and u.sup.(2) may be different is j=k-δm to j=k-ν. In all cases where the bits are different when the table is read, updating is possible by means of equation (10). The enable signal is simply generated by means of an XOR gate (see FIG. 6).
This serial realization limits the amount of circuitry, but slows down the speed. However, the path updating unit (PAU) can also be realized in parallel form, for example in (δ-ν) individual units per state. Then each unit only needs to compare one bit pair and to perform (at most) one table update for each symbol. If this is compared with the ACS unit, in which operations with real numbers must be performed, the ACS unit remains the bottleneck. The soft deciding Viterbi algorithm does not limit the speed.
The final decision does not differ from the conventional register exchange method; only the data transfer is greater by a factor of ns.
The Viterbi algorithm with analog decisions (SDVA) according to the invention works better than a conventional Viterbi decoder, demodulator or equalizer when concatenation is provided. This may include modulations with memory, for example a trellis coded modulation (TCM), or modulation methods with a constant envelope, such as CPM (continuous phase modulation) or TFM (tamed FM), channels with memories, for example filter channels with intersymbol interference (ISI), frequency-selective channels or also storage media, such as magnetic recordings; coding with memory, for example convolutional codes, and all possible combinations of these.
Some applications of practical interest will be described below. Applicant has investigated the performance of the Viterbi algorithm with analog value decision (SDVA) of the invention and compared the results with the SD-MAP algorithm, which is the optimal symbol-by-symbol receiver. Extensive computer simulations were also performed. The results have shown that the degradation of the SDV algorithm, compared with the SD-MAP algorithm is on the order of 0.2 dB. However, the gain compared with the hard decisions is 2 dB to 6 dB.
Concatenated coding with inner and outer convolutional codes also is very promising. With the inner codes the soft-quantized samples received are used which, in the case of channels with memory may possibly be improved by the use of channel state information. In connection with the receivers mentioned above, the outer decoder can also perform soft decision maximum likelihood decoding.
For example, the code with R=1/2 and ν=3 was used as inner code, and as outer code the punctured (perforated) code with R=2/3 and ν=3 (see Table 1). Both codes were separated by interleaving. The total code rate is R=Ri �R0 =1/3.
Because all the codes were derived from the same mother code, the trellis diagrams were the same and advantageously both the codes are correspondingly processed which utilized the same Viterbi algorithm in which the novel, soft-augmented receiver is used for the inner code and the conventional Viterbi algorithm for the outer code. A structure has already been provided in which interleaving, too, is utilized in a shared way in an efficient manner.
As a result the bit error curves are steeper and thus more promising. This holds true for the concatenation of two codes in comparison with a single convolutional code with a rate of 1/3 and the same receiver complexity. The gain is 0.7 dB at pb =10-5. Concatenation without the use of soft decisions is useless.
Regarding the optimal distribution between the inner and outer codes, several low-rate, rate-compatible punctured codes (RCPC codes) were used as inner codes and selected high-rate punctured codes in such a way, that the total rate R=Ri �R0 =1/3 was maintained (Ri ≦R0 ≦1). The most important parameters of the selected codes are listed in table 2 at the end of the description. Simulations have shown that in connection with low signal-to-noise ratios the outer code with the highest rate works best, as expected. However, in the SNR range of interest a distribution of Ri =1/2 and R0 =2/3 is the best.
In connection with convolutional codes, too, there is a possibility of soft code decoding in an optimal and elegant way. There are also simple block codes which can be decoded by means of soft decisions. Such codes are, for example, parity check codes or Golay codes. Such codes can be placed after the SDV algorithm and as step decoding they result in considerable improvement.
A possible use of this combination of convolutional codes is in the channel coding in the GSM system. In this case coding (at full rate speed) is usually done as follows:
A block of 260 net speech bits is grouped into three classes of sensitivity or sensibility. The 50 bits of the most sensitive class (class 1a) are increased by three parity bits in order to detect incorrigible errors. With one error usually the entire block is ignored and interpolation takes place. A "partial soft decision Viterbi algorithm" with parity check is now assumed, which supplies soft decisions only with the bits of class 1a and hard decision for the remaining bits of class 1b. It is then possible to perform a soft decision parity check which corrects additional errors, if required.
Alternately, in case errors were detected by means of the parity check, it is possible to perform maximum ratio combining with the "soft" value mk-1 .sup.(-1) of the previous block:
xk :=(xk +xk-1)/2
If necessary, this can also be improved by channel state information qk :
xk =(qk x k +qk-1 xk-1)/2
This results in a "soft" combination instead of a "hard" interpolation. Coded modulation has created great interest in recent years. The reason for this is bandwidth efficiency. In contrast to this, convolutional codes result in bandwidth extension which is proportional to the code rate if the number of elements of the symbol space remains unchanged.
In this connection the efficiency of the Ungerboeck code with four states and a rate of 2/3 was investigated. The signal may be considered to be corrupted by white Gaussian noise and is processed by means of the soft coding Viterbi algorithm. The modified Gaussian probability metric then reads (compared with equation (4)) as follows: ##EQU10## where xk.sup.(m) is the complex symbol of the m-th path corresponding to the trellis diagram, and yk is the complex value received at the same time k, where xk m and yk are written in complex notation. In the result the signal-to-noise ratio (SNR) of the soft decoding Viterbi algorithm is much better than at the input (normally by more than 3 dB). A decoder in the next stage operates much better with this improved signal-to-noise ratio (SNR).
Equalization offers a challenge with fast digital transmissions via time-dispersive channels, for example mobile radio channels. In this connection the Viterbi equalizer performs the desired maximum-likelihood sequence estimation. However, the difficulty in coded systems of the Viterbi equalizer supplying hard decisions to the outer decoder becomes obvious.
Therefore the SDV algorithm and the SD-MAP algorithm were investigated in connection with frequency-selective fading channels. For the channel a delay line with taps having (L+1) independent tap gaseous was assumed. This channel, which represents an idealization of the mobile multipath channel, can be considered to be the inner code. The modified Gaussian probability metric then reads (in comparison with equation (4)) as follows: ##EQU11## where xk.sup.(m) is the symbol for the m-th path corresponding to the trellis diagram, fk.sup.(1) is the 1-th amplification factor, where 0≦1≦L, yk is the received value at the same time k, and where xk.sup.(m), yk and fk.sup.(1) appear in complex notation. The value Es /N0 is the mean signal-to-noise ratio value. It was shown that the output variable of the SDV algorithm and the SDMAP algorithm almost have a Gaussian distribution, at least in the signal-to-noise ratio range of interest. This indicates that the frequency-selective fading channel is transformed into an AWGN channel if the spread is sufficiently large. A convolutional code of the rate 1/2 with a memory ν=3 was selected as outer code (see Table 1). With the SDV algorithm and the SDMAP algorithm each at pb =10-3, the gain is in the range of 4 dB, compared with the hard decisions. Similar results were derived for trellis codes as outer codes. As expected, the worse the channel, the larger the gain because of soft decisions. For this reason, a soft deciding Viterbi algorithm according to the invention can be used in a particularly advantageous manner especially in connection with fading channels.
TABLE 1______________________________________Code Parameters for Convolutional CodesCode i di cdi______________________________________R = 1/3 0 10 6 1 11 0 2 12 6 3 13 0 4 14 58R = 1/2 0 6 2 1 7 7 2 8 18 3 9 49 4 10 130R = 2/3 0 4 5 1 5 21.5 2 6 100 3 7 413 4 8 1657______________________________________ R = 1/3, R = 1/2: mother codes R = 2/3: punctured code (see Yasuda 1984) memory: ν = 3 generator polynoms: 15, 17, 13 (in octal) di : distance spectrum cdi : information weight spectrum (normalized cdi per each information bit)
TABLE 2______________________________________Code Parameters for Punctured Convolutional Codesinner code outer codeR dfree cdfree R dfree cdfree______________________________________1/2 6 2 2/3 4 54/9 6 0.5 3/4 4 41.32/5 7 1 5/6 3 12.68/21 7 0.25 7/8 2 0.6______________________________________ inner codes: punctured codes (see Hagenauer 1988) outer codes: punctured codes (see Yasuda 1984) memory: ν = 3 generator polynoms: 15, 17, 13 (in octal) dfree : distance spectrum cdfree : normalized nr. of bit errors of the minimumdistance path (per each information bit)
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These jeans are designed 100% to be worn without shirts. The waist is tailored such that the lowest abdominal muscle (that most humans don't have) is visible, all the while keeping the topmost pubic hair out of sight. It's a clever balancing act that has taken Swedish scientists the better part of a decade to perfect, but we think you'll find the results are worth it.
Sure, adults would look like morons dressed like Juno and Paulie, but toddlers in hoodies with sweatbands and short shorts? Adorable! Way cuter than Michael Cera and Ellen Page looked. This line could be sold most anywhere, from The Gap to Kmart to well-appointed gas stations. The best part is, entire outfits can be purchased for less than $20.
Now, you're probably thinking, "Wouldn't it be weird if I dressed my 4 year-old daughter up like a pregnant teenager?
Good question! No. It wouldn't.
Everyone knows that gay cowboys are the most fashionable cowboys, so why not find yourself in the same duds that Ennis and Jack rocked while swimming in the love that dare not speak its name? I can't think of a SINGLE reason why tough cowboys wouldn't want to look as good as these two do.
"I wish I knew how to quit…these rugged fashions!"
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Cinderella. Cinder-soot. Ash-girl.
A poor waif who, by no fault of her own, has a few cosmetic hygiene issues. She is merely the unfortunate receiver of brutal abuse and/or neglect by her stepmother and stepsisters. She is the Innocent Ragamuffin.
To which I say: no such thing.
I'm a fan of realism in my stories. People are flawed, layered individuals. Every Sunny Sally has a day when she snaps at her kids, treats the store clerk poorly, or ignores her Bible in favor of a romance novel. And every Debbie Downer has her moments of friendliness to a new neighbor or heartfelt devotion in prayer.
And ultimately, every single one of us is a sinner in need of salvation. All have fallen short of the glory of God (Romans 3:23) and all bear the curse of Adam's original sin (Romans 5:12-21).
This is one of my main issues with Cinderella. I can't take is the idea of a person being genuinely good from birth. Other than Jesus Christ.
Well, Cinderella is an archetypal figure. She's not meant to be a real person. However, archetypal fictional characters can still have powerful impacts on the real world. Cinderella is one of the most popular fairy tale characters in existence. She's featured on everything from lunchboxes to movies to computer games to clothing. She has her own castle in both Disney theme parks. All of this promotes the story of one little orphan's journey to royalty on the merits of her own righteousness and her incredible beauty.
Allow me to humbly spin the story another way:
Cinderella stank. She, her stepmother, and her stepsisters were all born into a filthy existence. The difference was, her family allowed themselves the luxury of fine perfumes, fancy clothes, and the best accommodations to disguise their true hideous nature. Cinderella was forced to remain in her filth, and then mocked for it. Bitterness grew in her heart.
One day, news came of a Prince in town. Rumor had it that this Prince was perfect: handsome, intelligent, charming, and compassionate. Everyone in the kingdom were invited to a grand ball, as the Prince sought members to fill his royal court. The stepsisters and stepmother dressed in their best finery to attend the glorious event. Cinderella was left in the squalor, her tears turning the greyish ash into a muddy slurry. A great winged Helper came to her, and beckoned her to the feast as she was. Cinderella shook her ratty head, and insisted she could only go if she was dressed as finely as everyone else. She couldn't face the ridicule of her sisters. The Helper relented, but told her it was only an illusion that would disappear at the stroke of midnight.
She went to the ball, dressed to the nines. Outwardly, Cinderella fit in with every other person there; inwardly, she was still painfully conscious of her stench and the ashes that covered her skin. Whispers circulated throughout the room. The Prince was overrated. He wasn't that great-looking. His clever tongue spoke in discomforting riddles. His heart seemed to be focused more on the wretched than the esteemed party guests. The words chilled Cinderella's heart. She had come hoping the Prince could rescue her.
When it came her turn to dance with him, Cinderella froze in fear. The guests were wrong. He was more than perfect. Pure holiness streamed from him like a beacon. And she was unworthy. The bitterness broke from her heart, to be replaced by despair. He couldn't rescue her–she'd be ashamed if he even touched her. Before the song could begin, the ash maiden turned and ran from the grand ballroom. With every step, her fine clothing faded. By the time she reached home, all that was left were rags and ashes.
The next day, news came that the Prince had found one to bring into his royal court. Every member of every household made themselves ready to receive him, soaking themselves in scented oils and wearing their best robes to hide the filth. Except for Cinderella. She was shut in the cellar. As always.
As the ash maiden sat on the cellar steps, she heard the sound of knocking. Joyful squeals erupted from her stepsisters–then Cinderella heard hisses of revulsion. A moment later, the cellar door opened, and a man, unkempt and shabbily dressed, was shoved down into the cellar. She walked hesitantly towards the figure, then gasped. It was the Prince. Even through the old clothes, his holiness shone like the noonday sun. Cinderella fell to the ground, hiding her face. Surely this had to be a mistake.
How could they have rejected him?
How could he here, when she was so foul?
Oh, she desperately needed him.
"Rise, my sister. Your sins have been forgiven. Rise, my bride."
A hand gently nudged her chin off the ground, and lifted her head. As she stared into the Prince's eyes, Cinderella felt an incredible peace and joy fill her spirit. The despair faded, and an overwhelming love took its place. Her skin became soft and white as snow. The smell of death was replaced by the fragrance of spring. She could hardly notice though. Her eyes were only filled with the Prince, as he led her out of the cellar, and into his royal court.
"But God demonstrates his own love for us in this: While we were still sinners, Christ died for us." (Romans 5:8)
"No, in all these things we are more than conquerors through him who loved us. For I am convinced that neither death nor life, neither angels nor demons,neither the present nor the future, nor any powers, neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord."
(Romans 8:37-39)
This is the best kind of Cinderella story.
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