FIELD OF THE INVENTION 
       [0001]    The present invention relates generally to signal encoding and in particular to speech encoding. 
       BACKGROUND 
       [0002]    For most of the period since the advent of wireless communication, information (e.g., audio, video) has been communicated through a process that involved continuously modulating a carrier signal with an information bearing signal, for example, an audio or video signal. 
         [0003]    In the 1990&#39;s progress in digital circuitry in terms of processing power and integrated circuit cost reduction allowed digital technology to supplant analog technology in cellular telephony. Digital technology is less prone to various types of analog signal degradation such as fading. Moreover, digital technology facilitates use of advanced techniques such as error-correction to achieve improved quality and data compression which results in lower bandwidth requirements for the same quality. 
         [0004]    For cellular telephony in particular the primary form of data to be communicated is speech audio. Typically, superior compression can be achieved by using a compression algorithm that is specifically designed for the type of data to be compressed. A compression technique that is especially suited to speech audio is known as Code-Excited Linear Prediction (CELP). CELP is based on a model of the human vocal apparatus, viz., the vocal cords and the vocal tract. In the model, the vocal tract is modeled by a discrete time signal filter that has a frequency response that mimics the resonances of the vocal tract, and sounds which in reality are generated by bursts of air passing the vocal cords and exciting acoustic resonances in the vocal tract are simulated (e.g., in a cell phone) by the output of the filter when a series of pulses are input into the filter. A discrete portion of speech (e.g., a frame or sub-frame) is then represented by a set of pulses and optionally by filter coefficients defining the filter. The set of pulses is described by the number of pulses, the magnitudes of the pulses, the positions of the pulses within the frame (or sub-frame), and the signs (±) of the pulses. As a person is speaking into his or her communication device, for each successive sub-frame the foregoing information must be transmitted; however, typically the information itself is not transmitted, rather the information is encoded and a code representing the information is transmitted. One way of doing this is to store each and every possible combination of the number, magnitudes, positions, and signs of the pulses in a codebook, with each possible combination having a unique address in the codebook, and to transmit the address in some form rather than transmitting the information about the pulses. A drawback of this approach is that if it is desired to achieve higher audio fidelity by allowing for more pulses or more precision in describing the positions or magnitudes of the pulses, the size of the codebook will increase thereby increasing the memory and search requirements for the codebook. 
       SUMMARY OF THE INVENTION 
       [0005]    According to one aspect, the invention provides a transmitting voice communication device that has an audio encoder that encodes audio coupled to an arithmetic encoder which further encodes the output of the audio encoder. According to certain embodiments the audio encoder is a CELP audio encoder. According other embodiments the audio encoder is a Discrete Cosine Transform (DCT) encoder. 
         [0006]    According to another aspect, the invention provides a receiving voice communication devices that has an arithmetic decoder that decodes received information encoding audio and passes output to an audio decoder which further decodes the output of the arithmetic decoder. According to certain embodiments the audio decoder is a CELP decoder and according to other embodiments the audio decoder is a DCT decoder. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0007]    The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout the separate views and which together with the detailed description below are incorporated in and form part of the specification, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the present invention. 
           [0008]      FIG. 1  is a block diagram of a communication system according to an embodiment of the invention; 
           [0009]      FIG. 2  is a block diagram of a communication device according to an embodiment of the invention; 
           [0010]      FIG. 3  is a high level flowchart of a method of processing audio to be transmitted according to an embodiment of the invention; 
           [0011]      FIG. 4  is a high level flowchart of a method of processing received digital audio signals according to an embodiment of the invention; 
           [0012]      FIG. 5  is a diagram illustrating the principle of arithmetic encoding for a binary sequence; 
           [0013]      FIG. 6  is a flowchart of an arithmetic encoder according to an embodiment of the invention; 
           [0014]      FIG. 7  is a flowchart of an arithmetic decoder according to an embodiment of the invention; 
           [0015]      FIG. 8  is a high level flowchart of a method of processing audio to be transmitted according to an alternative embodiment of the invention; 
           [0016]      FIG. 9  is a high level flowchart of a method of processing received digital audio signals according to an alternative embodiment of the invention; 
           [0017]      FIG. 10  is a front view of a wireless communication device according to an embodiment of the invention; 
           [0018]      FIG. 11  is a block diagram of the wireless communication device shown in  FIG. 10  according to an embodiment of the invention; and 
           [0019]      FIG. 12  shows how values used in arithmetic encoding are represented in binary fractions according to embodiments of the invention. 
       
    
    
       [0020]    Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the present invention. 
       DETAILED DESCRIPTION 
       [0021]    Before describing in detail embodiments that are in accordance with the present invention, it should be observed that the embodiments reside primarily in combinations of method steps and apparatus components related to digital speech communication. Accordingly, the apparatus components and method steps have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the embodiments of the present invention so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein. 
         [0022]      FIG. 1  is a block diagram of a communication system  100  according to an embodiment of the invention. The communication system  100  comprises a first voice communication device  102  and a second voice communication device  104  communicatively coupled through a communication network  106 . Both devices  102 ,  104  can have both transmit and receive capability or alternatively one of the devices  102 ,  104  can have only transmit capability and the other device only receive capability. The communication network  106  may, for example, include wireless radio channels and or fiber optic channels. The communication network  106  can for example comprise a cellular telephone network, a landline telephone network, a satellite telephone network, the Internet, a broadcast network such as a digital television network, or a digital radio network. 
         [0023]      FIG. 2  is a block diagram of an N TH  communication device  200  according to an embodiment of the invention. Either or both of the devices  102 ,  104  shown in  FIG. 1  can have the internal architecture shown in  FIG. 2 . Referring to  FIG. 2  the device  200  comprises a microphone  202  coupled through a first amplifier  204  to an analog-to-digital converter (A/D)  206 . The A/D  206  is coupled to an audio preprocessor  208 . The audio preprocessor  208  can, for example, perform noise filtering and echo cancellation. The audio preprocessor is coupled to a CELP encoder  210  such as an Algebraic CELP (ACELP) encoder. The ACELP is a form of Code-Excited Linear Predictive (CELP) encoder that uses a specially structured excitation codebook. Each code vector from such a codebook consists of a specified number of integer-valued pulses at specific positions within a frame (or sub-frame). The CELP encoder  210  determines a small set of vocal apparatus model parameters, including the pulse information (i.e., excitation code vector) described above which describes a driving function for the model vocal apparatus. The pulse information including (1) the number of pulses per frame (or sub-frame), (2) the magnitudes of the pulses, (3) the locations of the pulses, and (4) the signs (±) of the pulses that are produced by the CELP encoder  210  is used to represent speech audio. 
         [0024]    If n is the number of pulse positions in a sub-frame and m is an upper bound on the sum of the integer pulse magnitudes for the sub-frame, then the number of pulses in the sub-frame denoted by k is bounded as follows: 
         [0000]      1 ≦k ≦min( m,n ) 
         [0000]    The number of possible sets of pulse positions in the sub-frame is given by: 
         [0000]    
       
         
           
             
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         [0000]    The number of possible ways to distribute the energy in the pulses is given by: 
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         [0000]    and the number of combinations of different signs of the pulses is given by 2 k . 
         [0025]    Accordingly, the number of different unique sets of pulses for a sub-frame is given by: 
         [0000]    
       
         
           
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         [0000]    The preceding expression also gives the number of unique codes that would need to be stored if the prior art code-book approach were used. 
         [0026]    Referring again to  FIG. 2  it is seen that the CELP encoder  210  is coupled to a pulse information encoder  211 . The pulse information encoder  211  serves to format the information produced by the CELP encoder  210  in a format acceptable to an arithmetic encoder  212 . In preparation for arithmetic encoding, the positions of pulses can be represented by a binary vector that includes a one for each position where there is a pulse. This may be the native format used by the CELP encoder in which case no reformatting is necessary. 
         [0027]    The magnitudes of the pulses can be represented by a magnitude vector in which each element is an integer representing the magnitude of a pulse. Such magnitude vectors can be converted to binary vectors (i.e., vectors in which each element is a single bit, viz., 0 or 1) by the pulse information encoder  211  by replacing each magnitude integer by a sequence of zeros numbering one less than the magnitude integer followed by a one. In as much as the last bit in the binary vector would always be a one, it can be ignored. The following are examples (for m=6 and k=3) of magnitude vectors at the left and corresponding binary vectors at the right that result from the foregoing conversion process: 
         [0000]    
       
         
           
             
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         [0028]    The binary vectors can then be encoded using the arithmetic encoder  212 . The magnitude vectors can be recovered, after arithmetic decoding, by counting the number of zeros preceding each one. 
         [0029]    The signs of the pulses can be represented by a binary vector in which the bit value represents the sign, e.g., a bit value of 1 can represent a negative sign, and a bit value of 0 a positive sign. If the CELP encoder  210  outputs sign information differently, the pulse information encoder  211  can reformat the sign information in the foregoing manner. 
         [0030]    The pulse information encoder  211  is coupled to the arithmetic encoder  212 . The arithmetic encoder  212  encodes the pulse information received from the CELP encoder  210  through the pulse information encoder  211 . The operation of the arithmetic encoder  212  is described more fully below. By using an arithmetic encoder, storing a large codebook is avoided. 
         [0031]    The arithmetic encoder  212  is coupled to a channel encoder  217  which is coupled to a transmitter  214  of a transceiver  216 . The transceiver  216  also includes a receiver  218 . The receiver  218  is coupled to an arithmetic decoder  220  through a channel decoder  219 . The arithmetic decoder  220  outputs pulse information. The operation of the arithmetic decoder  220  is described more fully below. The arithmetic decoder  220  is coupled through a pulse information decoder  221  to a CELP decoder  222 . The pulse information decoder  221  performs the inverse of the processes performed by the pulse information encoder  211 . The CELP decoder  222  reconstructs a digital representation of speech audio (digitized audio signal) using the pulse information. The CELP decoder  222  is coupled to a digital-to-analog converter (D/A)  224  that is coupled through a second amplifier  226  to a speaker  228 . 
         [0032]      FIG. 3  is a high level flowchart of a method  300  of processing audio to be transmitted according to an embodiment of the invention. In block  302  audio is detected with a microphone. In block  304  the audio is digitized. In block  306  the audio is pre-processed which can for example comprise filtering and echo canceling. In block  308  the audio is encoded with a CELP speech encoder. In block  310  the audio pulse information output of the CELP speech encoder is encoded with an arithmetic encoder. In block  312  the audio is channel encoded and in block  314  the channel encoded audio is transmitted. 
         [0033]      FIG. 4  is a high level flowchart of a method  400  of processing received digital audio signals according to an embodiment of the invention. In block  402  channel encoded audio is received. In block  404  the audio is decoded with a channel decoder. In block  406  the audio is decoded with an arithmetic decoder. In block  408  the output of the arithmetic decoder is decoded with a CELP speech decoder. In block  410  the output of the CELP speech decoder is converted to an analog signal, and in block  412  the analog signal is used to drive a speaker. 
         [0034]    According to alternative embodiments of the invention, parts of the methods shown in  FIGS. 3-4  are used in a transcoder in which case detecting audio with a microphone or outputting audio through a speaker will not be done. Such a transcoder can be used at a gateway between two disparate networks for example. 
         [0035]      FIG. 5  is a diagram  500  illustrating the principle of arithmetic encoding for a binary sequence. The diagram  500  is divided into three columns. Each column corresponds to a bit position in a bit sequence to be encoded, with the column at the left corresponding to the first bit position. The diagram can be used for any 3-bit sequence. There are 8 possible 3-bit sequences. The diagram  500  is based on the assumption that there is a fixed probability of 2/3 that any bit in the sequence is a 0 and consequently a fixed probability of 1/3 that any bit is a 1. This is just an example for purposes of illustration. The code space is the domain from zero to one, [0,1). Each possible 3-bit sequence is to be encoded as a binary fraction in the range from zero to one. The diagram  500  works as follows. The left hand column is divided into an area for sequences that start with zero and an area for sequences that start with one. The relative size of the areas depends on the probability of emitting the respective values (e.g., 2/3 for 0 and 1/3 for 1). In each successive column the areas from the preceding column are again apportioned to binary one and binary zero according to their respective probabilities. Thus, the code space is most finely divided in the last (right side) column. Any given 3-bit sequence corresponds to a particular area of the last column. A fraction that falls within the area corresponding to a 3-bit sequence is used as a code for that 3-bit sequence. The fraction is represented in binary. Generally speaking, the smaller the area assigned to a particular 3-bit sequence, the longer is the code required to represent that sequence by a binary fraction. 
         [0036]    Although in the foregoing the probability of ones and zeros is assumed to remain fixed, alternatively the probabilities can vary. In certain embodiments total number of ones (or zeros) is known a priori or separately transmitted beforehand, and at any bit position in a sequence being encoded the probability of a zero is computed as the ratio of the number of zeros yet to be encountered to the total number of bits yet to be processed. 
         [0037]    In the example shown in  FIG. 5  different 3-bit sequences map to regions of the code space of different sizes. However if one considers all the different n-bit sequences having a predetermined number, say k&lt;n ones, and if the probability of a zero is computed as the aforementioned ratio, then it is the case that all of the different n-bit sequences having k ones will map to regions of equal size. In other words the code space will be portioned into equal size regions. The number of regions N P (n,k) representing the number of possible sets of pulse positions is given by: 
         [0000]    
       
         
           
             
               
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         [0038]    However, in practice, the width of the code space interval corresponding to a source sequence may not exactly be equal to 1/N P (n,k) because of the rounding operations necessary to perform fixed-precision arithmetic. The actual width of the interval corresponding to a source sequence depends on the sequence itself and the precision used in the calculations. While this is cumbersome to compute, a bound can be derived for the minimum length of the code words I P (n,k,w) based on a few conservative assumptions. For example, it can be shown that (see Appendix I): 
         [0000]        I   P ( n, k, w )=┌log 2    N   P ( n, k )+Ω( n, k, w )┐, where 
         [0000]      Ω( n, k, w )=log 2 (1/1−( n/k )2 −(w+1) )+log 2 (1/1−( n− 1/ k− 1)2 −(w+1) )+ . . . +log 2 (1/1−( n−k+ 1/1)2 −(w+1) )+log 2 (1/1−( n/n−k )2 −(w+1) )+log 2 (1/1−( n− 1/ n−k− 1)2 −(w+1) )+ . . . +log 2 (1/1−( k+ 1/1)2 −(w+1) ) 
         [0039]    In the equations above, w represents a precision parameter, i.e., (starting) positions, and (the widths of the) intervals in the code space are stored using w+2 and w+1 bits respectively. In general, in order to compute such positions (denoted x) and intervals (denoted y) in the code space, binary registers that are up to 2*(w+2) bits wide will need to be used assuming that the input symbol probabilities (e.g., probabilities of binary digits 0 and 1) are also represented using (w+1) bits. Binary registers of such width are used to store a numerator of a parameter z that is discussed below in the context of  FIGS. 6-7  and is used in calculating intervals and positions in the code space. According to embodiments of the present invention, arithmetic encoders and decoders produce and decode code words I P (n,k,w) bits long using at least 2*(w+2) bits, and for efficiency sake, preferably less than 2*(w+2)+8 bits, more preferably less than 2*(w+2)+3 bits, and even more preferably exactly 2*(w+2) bits. It will not always be possible to use exactly 2*(w+2) bits because concessions may have to be made to other demands, e.g., other processes using a shared processor. 
         [0040]      FIG. 6  is a flowchart  600  of an arithmetic encoder according to an embodiment of the invention, and  FIG. 7  is a flowchart  700  of an arithmetic decoder according to an embodiment of the invention. The flowcharts in  FIG. 6  and  FIG. 7  can be used respectively to encode and decode the positions and magnitudes of the pulses. The number of pulses and the signs of the pulses can also be encoded and decoded using appropriately configured arithmetic encoders and arithmetic decoders respectively. A single code word can be computed to represent collectively the number of pulses, the positions, the magnitudes, and the signs of the pulses. Alternately, individual code words can be computed to represent separately the number of pulses, the positions, the magnitudes, and the signs of the pulses, and optionally these individual code words can be concatenated to form a single code word. Between the two extremes above any other combination is also possible, for example, a single code word can be computed to represent the positions and magnitudes together, and two individual code words can be computed to represent the number of pulses and the signs separately. The variables used in  FIG. 6  and  FIG. 7  are defined in Table I below: 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                   
                   
                 Upper 
               
               
                 Symbol 
                 Meaning 
                 bound 
               
               
                   
               
             
             
               
                 u i   
                 i th  information bit 
                 1 
               
               
                 i 
                 index for the information word α: u 1 , u 2 , . . . , u n   
                 n 
               
               
                 v j   
                 j th  code bit 
                 1 
               
               
                 j 
                 index for the codeword β: v 1 , v 2 , . . . , V l   
                 l 
               
               
                 w 
                 precision parameter 
                 design 
               
               
                   
                   
                 value 
               
               
                 x 
                 (w + 2) least significant bits of the start of the 
                 2 w+2  − 1 
               
               
                   
                 interval corresponding to α and its prefixes 
               
               
                 y 
                 (w + 1) least significant bits of the width of the 
                 2 w+1  − 1 
               
               
                   
                 interval corresponding to α and its prefixes 
               
               
                 n 
                 number of information bits 
                 design 
               
               
                   
                   
                 value 
               
               
                 l 
                 number of code bits 
                 design 
               
               
                   
                   
                 value 
               
               
                 k 
                 number of 1&#39;s in α, i.e., the weight of α 
                 design 
               
               
                   
                   
                 value 
               
               
                 ñ 
                 number of bits yet to be scanned in α 
                 n 
               
               
                 ñ 0   
                 number of 0&#39;s yet to be scanned in α 
                 n − k 
               
               
                 z 
                 value of └(2yñ 0  + ñ)/2ñ┘ 
                 y 
               
               
                 e 
                 ejected value from x, a code bit plus a possible carry 
                 3 
               
               
                 nb 
                 next bit to be stored away (or transmitted) 
                 1 
               
               
                 rb 
                 run bit, 0 if there is a carry and 1 if there is none 
                 1 
               
               
                 rl 
                 run length 
                 l 
               
               
                   
               
             
          
         
       
     
         [0041]    A mathematical foundation of arithmetic encoding is given in the first part of Appendix I. Referring to  FIG. 6  the encoding algorithm will be described. In block  602  the variables i, j, x, y, rl, ñ, and ñ 0  are initialized. Recall that in  FIG. 5  the code space was the interval [0,1). The value 2 w  to which y is initialized in some sense represents the upper bound  1  of the code space. 2 w  can be viewed as a scale factor, and using such an integer scale factor allows the arithmetic coding to be performed using fixed precision integer arithmetic, which means that less computing power is needed to perform the encoding. 
         [0042]    After block  602 , decision block  604  tests if there are any remaining ones in the sequence α being encoded. If so the flowchart branches to block  606  in which the quantity z is computed, the number of information bits yet to be coded ñ is decremented, and the index i is incremented. Initially the outcome of decision block  604  is positive. The quantity z is related to the size of the portion of the code space that is associated with a zero value for a current bit position in the sequence being encoded and is a fraction of the portion of the code space associated with a previous bit. This can be understood by referring to second column of  FIG. 5  in which it is seen that the regions of the first column associated with zero and one are further subdivided in column two into regions proportional to the probability of each bit value.  FIG. 5  is constructed using a fixed probability of 2/3 for a zero bit and 1/3 for 1 bit throughout the sequence. The arithmetic encoder as shown in  FIG. 6  works differently. In particular the probability of a zero bit is set to the number of zero bits remaining divided by the total number of bits remaining. This is accomplished in the computation of z in block  606 . Given the region corresponding to a previous bit represented by the integer y, the region corresponding to a zero bit at the current position is obtained by multiplying y with the probability of a zero bit and rounding the result to the nearest integer. As shown, a bias of ½ and the floor function are used for rounding to the nearest integer. Alternatively, fixed probabilities can be used. For example if the pulse sign information is to be encoded separately, and there is an equal probability of pulses being positive and negative, the computation of z can be based on fixed probabilities of zero and one bits equal to ½. 
         [0043]    Next the flowchart  600  reaches decision block  608  which tests if the current bit in the sequence being encoded, identified by index i, is a zero or one. If the current bit is a zero then in block  610  the value y is set equal to z and ñ 0  (the number of zeros yet to be encountered) is decremented. The value of x is unchanged. On the other hand if the current bit is a one then in block  612  y is set equal to a previous value of y minus z and x is set equal to a previous value of x plus z. The new value of y is a proportion of the previous value of y with the proportion given by the probability of the current bit value (zero or one). x and y are related respectively to the starting point and the width of the area within the code space [0,1) as represented by [0,2 w ) that corresponds to the bit sequence encoded so far. 
         [0044]    After either block  610  or  612  decision block  614  is reached. Decision block  614  tests if the value of y is less than 2 w . (Note that blocks  606 ,  610  and  612  will reduce the value of y.) If so then in block  616  the value of y is scaled up by a factor of 2 (e.g., by a left bit shift), the value of e is computed, and the value of x is reset to 2(x mod  2   w ). Using the mod function essentially isolates a portion of x that is relevant to remaining, less significant code bits. Because both y and x are scaled up in block  616  in a process referred to as renormalization, even as the encoding continues and more and more information bits are being encoded, the full value of 2 w  is still used as the basis of comparison of x in the floor function to determine the value of the code bits. Similarly, the full value of 2 w  is still used as the basis of comparison of y in the decision block  614 . 
         [0045]    After block  616 , decision block  618  tests if the variable e is equal to 1. If the outcome of decision block  618  is negative, then the flowchart  600  branches to decision block  620  which tests if the variable e is greater than 1 (e.g., if there is an overflow condition). If not, meaning that the value of e is zero, the flowchart  600  branches to block  622  wherein the value of the run bit variable rb is set equal to 1. 
         [0046]    Next the flowchart  600  reaches block  624  in which the code bit index j is incremented, the code bit v j  is set equal to value of nb, and then nb is set equal to e. Note that for the first two executions of block  624 , j is set to values less than one, so the values of v j  that are set will not be utilized as part of the output code. 
         [0047]    When the outcome of decision block  618  positive the flowchart  600  will branch through block  626  in which the run length variable rl is incremented and then return to decision block  614 . Decision block  628  tests if the run length variable rl is greater than zero—the initial value. If so then in block  630  the index j is incremented, code bit v j  is set to the run bit variable rb, and the run length rl is decremented, before returning to decision block  628 . When it is determined in decision block  628  that the run length variable rl is zero the flowchart  600  returns to block  614 . 
         [0048]    If the outcome of decision block  620  is positive, i.e., an overflow condition has been detected, then the flowchart  600  branches to block  632  in which the nb variable is incremented, the rb variable is zeroed, and the e is decremented by 2, after which the flowchart  600  proceeds with block  624 . 
         [0049]    If it is determined in decision block  604  that only zeros remain in the sequence being encoded, then the flowchart  600  branches to block  634  in which the value of the variable e is computed as the floor function of x divided by 2 w . Next decision block  636  tests if e is greater than 1. If so then in block  638  the next bit variable nb is incremented, the run bit variable rb is set equal to 0, and the variable e is decremented by 2. If the outcome of decision block  636  is negative, then in block  640  the run bit variable rb is set equal to 1. After either block  638  or  640 , in block  642 , the index j is incremented, the code bit v j  is set equal to the next bit variable nb, and the next bit variable nb is set equal to e. 
         [0050]    Next decision block  644  tests if the run length variable rl is greater than zero. If so then in block  646  the index j is incremented, the code bit v j  is set equal to the run bit variable rb, and the run length variable rl is decremented, after which the flowchart  600  returns to block  644 . 
         [0051]    After block  644  in block  648  the index j is incremented, and the code bit v j  is set equal to the next bit variable nb. Next decision block  650  tests if the index j is less than the code length l. If so then block  652  sets remaining code bits to 1. When j reaches l the encoding terminates. 
         [0052]    Referring to  FIG. 7  a flowchart  700  of an arithmetic decoding method corresponding to the encoding method shown in  FIG. 6  will be described. In block  702  the variables i, j, x, y, ñ, and ñ 0  are initialized. Decision block  704  tests if y is less than 2 w . When, as is the case initially, this is true, the flowchart  700  branches to decision block  706  which tests if the index j is less than l. When, as is the case initially, this is true, the flowchart  700  braches to block  708  in which j is incremented, and the variable x is reset to 2x+v i . Basically, successive executions of block  708  build up the value of x based on the values of the code bits, taking into account the position (significance) of the bits. After block  708  in block  710  the value of y is similarly increased by multiplying by two. After block  710  the flowchart  700  returns to decision block  704 . When the end of the codeword is reached, i.e., after j reaches l, the outcome of decision block  706  will be negative, and in this case, in block  712  x is set to 2x+1. This is equivalent to reading in a code bit with a value of 1. 
         [0053]    After block  712  block  710  is executed. When it is determined in decision block  704  that y is not less than 2 w , the flowchart  700  branches to block  714  which computes the value of z as shown, decrements the number of information bits yet to be decoded n, and increments the index i which points to bits of the decoded sequence. Next decision block  716  tests if x is less than z. If not then in block  718  an i th  decoded bit u i  is set equal to one, x and y are decremented by z to account for the parts of x and y represented by the i th  bit just decoded. If decision block  716  determines that x is less than z then in block  720  the i th  decoded bit u i  is set equal to zero, y is set equal to z, and the number of zeros yet to be encountered no is decremented to account for the zero bit u i  just decoded. 
         [0054]    After either block  718  or  720  decision block  722  tests if the number of zeros remaining is less than the total number of bits remaining. If the outcome of block  722  is affirmative, the flowchart  700  loops back to decision block  704 . If the outcome of block  722  is negative, the flowchart branches to decision block  724  which tests if i is less than n. If so block  726  zero fills the remaining bits. When the outcome of decision block  724  is negative the decoding process terminates. 
         [0055]      FIG. 8  is a high level flowchart of a method  800  of processing audio to be transmitted according to an alternative embodiment of the invention. In block  802  audio to be encoded is input. The audio can, for example, be input through a D/A from a microphone. Optionally the audio can be passed through a noise filter or echo canceller. In block  804  a DCT is applied to the audio. One type of DCT that may be used is the Modified DCT (MDCT). The MDCT is distinguished by reduction of encoding artifacts. For many audio signals, DCTs such as the MDCT only produce a few coefficients of significant magnitude. In block  806  the output of the DCT is quantized, e.g., using an uniform scalar quantizer. Quantization will result in many low magnitude coefficients being set to zero, such that, for many audio signals, there will only be a relatively small number of non-zero DCT coefficients. Because of this, the quantized output of the DCT (e.g., MDCT) can be efficiently encoded, as will be described below, using arithmetic encoding. 
         [0056]    In block  808  information as to the position of any non-zero coefficients is encoded in a first binary vector. The length of the first binary vector is equal to the number of DCT coefficients, and each bit in the first binary vector is set to a one or a zero depending on whether the corresponding (by position) coefficient of the quantized DCT output is non-zero or zero. 
         [0057]    In block  810  the signs of the non-zero quantized DCT coefficients are encoded in a second binary vector. The second binary vector need only be as long as the number of non-zero quantized DCT coefficients. Each bit in the second binary vector is set equal to a zero or a one depending on whether the corresponding non-zero quantized DCT coefficient is negative or positive. As discussed above arithmetic coding and decoding of binary vectors encoding sign information can be based on assumed fixed probabilities of ½ for both zero and one, and therefore it is not necessary to transmit the number of ones (or zeros) in such vectors. 
         [0058]    In block  812  the magnitudes of the non-zero quantized DCT coefficients are encoded in a third binary vector. The method of encoding magnitudes described above with reference to the pulse information encoder  211  is suitably used. Note that according to certain embodiments the sum of the magnitudes of the coefficients is a fixed (design) value, and in such cases the number of zeros in binary vectors encoding the magnitudes will also be fixed and therefore need not be transmitted. 
         [0059]    In block  814  one or more of the first through third binary vectors are encoded using an arithmetic encoder. Two or more of the first through third binary vectors can be concatenated and encoded together by the arithmetic encoder, or the binary vectors can be encoded separately by the arithmetic encoder. In block  816  the number of non-zero DCT coefficients are transmitted. The number of non-zero DCT coefficients can be encoded (e.g., arithmetic encoded or Huffman encoded) prior to transmission. In block  818  the encoded binary vectors are transmitted. 
         [0060]      FIG. 9  is a high level flowchart of a method  900  of processing received digital audio signals according to an alternative embodiment of the invention. The method  900  decodes the encoded vectors generated by the method  800 . In block  902  the number of non-zero DCT coefficients that was transmitted in block  816  is received (and decoded). In block  904  the arithmetic encoded vector(s) transmitted in block  818  are received. In block  906  the encoded vectors are decoded with an arithmetic decoder. In block  908  the positions of the non-zero coefficients are read from the first binary vector. In block  910  the magnitudes of the non-zero coefficients of the quantized DCT are decoded from the third binary vector. In block  912  signs of the non-zero coefficients of the quantized DCT are read from the second binary vector. In block  914  the quantized DCT vector is reconstructed based on the information obtained from the first through third binary vectors, and in block  916  the inverse DCT transform is performed on the reconstructed quantized DCT vector. In block  918  a sub-frame of audio is regenerated from the output of the inverse DCT. The flow charts in  FIGS. 8-9  can also be used to process residual audio signals, that is, the difference between an original audio signal and a coded version of the original, as encountered often in embedded audio coders. 
         [0061]      FIG. 10  is a front view of a wireless communication device, in particular a cellular telephone handset  1000  according to an embodiment of the invention. The handset  1000  includes a housing  1002  supporting an antenna  1004 , display  1006 , keypad  1008 , speaker  1010  and microphone  1012 . Although a “candy bar” form factor handset is shown in  FIG. 10 , one skilled in the art will appreciate that the encoders and decoders disclosed herein can be incorporated in a myriad of devices of different form factors. 
         [0062]      FIG. 11  is a block diagram of the wireless communication device  1000  shown in  FIG. 10  according to an embodiment of the invention. As shown in  FIG. 11 , the wireless communication device  1000  comprises a transceiver module  1102 , a processor  1104  (e.g., a digital signal processor), an analog to digital converter (A/D)  1106 , a key input decoder  1108 , a digital to analog converter (D/A)  1112 , a display driver  1114 , a program memory  1116 , and a workspace memory  1118  coupled together through a digital signal bus  1120 . 
         [0063]    The transceiver module  1102  is coupled to the antenna  1004 . Carrier signals that are modulated with data, e.g., audio data, pass between the antenna  1004  and the transceiver module  1102 . 
         [0064]    The microphone  1012  is coupled to the A/D  1106 . Audio, including spoken words and ambient noise, is input through the microphone  1012  and converted to digital format by the A/D  1106 . 
         [0065]    A switch matrix  1122  that is part of the keypad  1008  is coupled to the key input decoder  1108 . The key input decoder  1108  serves to identify depressed keys and to provide information identifying each depressed key to the processor  1104 . 
         [0066]    The D/A  1112  is coupled to the speaker  1010 . The D/A  1112  converts decoded digital audio to analog signals and drives the speaker  1010 . The display driver  1114  is coupled to the display  1006 . 
         [0067]    The program memory  1116  is used to store programs that control the wireless communication device  1000 . The programs stored in the program memory  1116  are executed by the processor  1104 . The workspace memory  1118  is used as a workspace by the processor  1104  in executing programs. Methods that are carried out by programs stored in the program memory  1116  are described above with reference to  FIGS. 1-9 . The program memory  1116  is a form of computer readable media. Other forms of computer readable media can alternatively be used to store programs that are executed by the processor  1104 . 
         [0068]    In the foregoing specification, specific embodiments of the present invention have been described. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the present invention as set forth in the claims below. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of present invention. The benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential features or elements of any or all the claims. The invention is defined solely by the appended claims including any amendments made during the pendency of this application and all equivalents of those claims as issued. 
       Appendix I 
       [0069]    A) Mathematical Foundation of Arithmetic Coding: 
         [0070]    In arithmetic coding, each information word to be coded is assigned a unique subinterval within the unit interval [0, 1). The computation of this interval can be performed recursively with the knowledge of the probabilities of the symbols within the information word. A point within the interval is then selected, and a fractional representation of this point is used as the codeword. 
         [0071]    Mathematically, let α denote a binary information word and l(α)=[x(α), x(α)+y(α)) denote the interval corresponding to α where x(α) denotes the start of the interval and y(α) denotes the width of the interval. When α is just the empty sequence ε, we define 
         [0000]        x (ε)=0.0 and y(ε)=1.0, 
         [0000]    so that l(ε)=[0, 1). If the interval corresponding to α is known, then the intervals corresponding to α0 and α1 (i.e., the concatenation of α and either 0 or 1 respectively) can be computed as follows. 
         [0000]        x (α0)= x (α), 
         [0000]        y (α0)= y (α)  P (0|α), 
         [0000]        x (α1)= x (α)+ y (α)  P (0|α), and 
         [0000]        y (α1)= y (α)  P (1|α)= y (α) (1− P (0|α))= y (α)− y (α)  P (0|α), 
         [0000]    where P(0|α) and P(1|α) (=1−P(0|α)) denote respectively the probabilities of a 0 or 1 bit following the bit sequence α. Using the notation z(α)=y(α) P(0|α) in the above equations, we have 
         [0000]        x (α0)= x (α), 
         [0000]        y (α0)= z (α), 
         [0000]        x (α1)= x (α)+ z (α), and 
         [0000]        y (α1)= y (α)− z (α). 
         [0072]    Computation of the interval l(α) corresponding to α using the above recursive equations requires infinite precision. In arithmetic coding, rounding and scaling (or renormalization) operations are used which allow the computation of l(α) to be performed using finite precision arithmetic. However, the computed interval is now only an approximation of the actual interval. Let us define the integers x*(α), y*(α), L(α), and w so that x(α) and y(α) can be expressed using finite precision (i.e., using L(α)+w bits) as 
         [0000]        x (α)= x *(α)/2 L(α)+w , and 
         [0000]        y (α)= y *(α)/2 L(α)+w . 
         [0073]    The recursive equations for the computation of the interval l(α) are now reformulated as follows. For the empty sequence ε, we define 
         [0000]        x *(ε)=0,  y *(ε)=2 w , and  L (ε)=0. 
         [0074]    If x*(α), y*(α), and L(α) are known for a sequence α, then we have 
         [0075]    for the sequence α0: 
         [0000]        z *(α)=└ y *(α) P (0|α)+1/2┘, 
         [0000]        x *(α0)= x *(α)2 d0 , 
         [0000]        y *(α0)= z *(α)2 d0 , and 
         [0000]        L (α0)= L (α)+ d 0, 
         [0076]    where d0 is an integer for which 2 w ≦y*(α0)&lt;2 w+1 ; and 
         [0077]    for the sequence α1: 
         [0000]        z *(α)=└ y *(α) P (0|α)+1/2┘, 
         [0000]        x *(α1)=( x *(α)+ z *(α))2 d1 , 
         [0000]        y *(α1)=( y *(α)− z *(α))2 d1 , and 
         [0000]        L (α1)= L (α)+ d 1, 
         [0078]    where d1 is an integer for which 2 w ≦y*(α1)&lt;2 w+1 . 
         [0079]    In the above equations, the rounding operation used in the computation of z*(α) ensures that it is expressed in finite precision (w+1 bits). Also, the choice of d0 (respectively d1) used in scaling y*(α0) (respectively y*(α1)) ensures that the scaled interval width has enough precision (w+1 bits) for further subdivision. The precision parameter w is a design value and should be chosen to suit the coding application. A choice of w=14, for example, provides enough precision for general applications and also allows standard integer arithmetic to be used in computing the codeword. 
         [0080]    The binary fractional representations of x(α) and y(α) are shown in  FIG. 12 . Since y*(α) is always bounded by 2 w ≦y*(α)&lt;2 w+1 , the binary fractional representation of y(α) has L(α)−1 leading zeros followed by w+1 least significant bits. The storage of y(α) therefore requires only a (w+1) bit register. Unlike y(α), x(α) is not bounded and can keep increasing in length as more and more information bits are coded. However, its binary representation can be thought of as consisting of four parts: 1) the most significant bits which will not undergo any further change and therefore can be stored away in a suitable medium or transmitted, 2) the next bit (to be stored away), 3) a run of 1&#39;s, and 4) the working end of (w+1) least significant bits. The next bit, the run length, and the working end can be stored in suitable registers. Both the next bit and the run bit may undergo a change if there is a carry (overflow condition) out of the working end. 
         [0081]    B) Bounding the Codeword Length: 
         [0082]    Consider the encoding of an n-bit sequence using the flowchart  600  in  FIG. 6 . At any position within the sequence, the probability of a 0 is defined by the ratio  n   0 /  n  which can be exactly represented by the integers  n   0  and  n . Therefore, the only source of error in computing x(α) and y(α) arises due to the rounding operation in the computation of z*(α). Using the recursive equations above and the inequality g−1&lt;└g┘≦g for g real, we can express 
         [0000]        y *(α0)/2 L(α0)+w &gt;( y *(α) P (0|α)−1/2))/   2     L(α)+w , and 
         [0000]        y *(α1)/2 L(α 1)+w≧( y *(α) P (1|α)−1/2))/2 L(α)+w . 
         [0083]    Combining the two expressions, we have 
         [0000]        y *(α u )/2 L(αu)+w ≧( y *(α) P ( u|α )−1/2))/2 L(α)+w    
         [0000]    where u is a 0 or 1. The above expression can be rewritten as 
         [0000]    
       
         
           
             
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         [0084]    Since y*(α)≧2 w , we have 
         [0000]    
       
         
           
             
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         [0000]    where δ=2 −(w+1) . Applying the above relationship recursively to the input bit sequence (i.e., information word) α=u 1 , u 2 , . . . , u n  and recalling that y(ε)=1, we have 
         [0000]    
       
         
           
             
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         [0085]    The expression P(u 1 |ε)P(u 2 |u 1 ) . . . P(u n |u 1 u 2  . . . u n−1 ) represents the probability P(α) of the sequence α and is also the ideal interval width. If α is a n-bit sequence with k ones and if the probability of a zero at any position is given by ñ 0 /ñ, then it can be shown that P(α)=1/N P (n,k) where 
         [0000]    
       
         
           
             
               
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         [0086]    Simplifying the notation by replacing P(u i |u 1 u 2  . . . u i−1 ) by P i , we have 
         [0000]    
       
         
           
             
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         [0087]    Each term of the form 
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         [0000]    reduces the interval width from the ideal value P(α) with the greatest reduction occurring for the smallest value of P i . While the actual set of probabilities {P i , i=1, 2, . . . , n} depends on the particular n-bit sequence, the following set of n probabilities {k/n, k−1/n−1, . . . , 1/n−k+1, n−k/n, n−k−1/n−1, . . . , 1/k+1} provides a lower bound for any sequence α. The codeword length l P (n,k,w) should be chosen such that 2 −l     P     (n, k, w) ≦y(α) for unique decodability. Substituting for P(α), {P i , i=1, 2, . . . , n}, taking logarithm to the base 2, and rearranging the terms, the minimum codeword length is given by 
         [0000]        l   P ( n, k, w )=┌log 2    N   P ( n,k )+Ω( n,k,w )┐, where 
         [0000]      Ω( n,k,w )=log 2 (1/1−( n/k )2 −(w+1) )+log 2 (1/1−( n− 1/ k− 1)2 −(w+1) )+ . . . +log 2 (   1 / 1   −( n−k+ 1 / 1   )2 −(w+1) )+log 2 (1/1−( n/n−k )2 −(w+1) )+log 2 (1/1−( n− 1/ n−k− 1)2 −(w−1) )+ . . . +log 2 (1/1−( k+ 1/1)2 −(w+1) )
A communication system ( 100) includes devices ( 102, 104, 200) for transmitting and receiving digital audio. The devices use audio encoders ( 210, 804) and decoders ( 222, 916) such as ACELP or DCT/IDCT to compress and decompress audio and use arithmetic encoders ( 212) and decoders ( 220) to encode and decode the compressed audio on-the-fly (without a codebook of pre-stored codes).