'FEC limit BER' in communication systems
" Why do many communication systems specify BER requirements to be \$10^{-12}\$ to \$10^{-9} ~~~?~\$  "


Why not worse or better?

There is no absolute answer as the error probability can never be zero forever, but can be zero in some finite time.  The answer lies in the cost/benefit ratio of an improvement and depends on the value and redundancy of such data.  We cannot put a universal cost factor on this exponent for all cases but just assume for now, it is based on historical technology limits with a sensitivity to cost. 

We know bandwidth has costs as well as channel capacity and redundancy has an added cost. Depending on the isolation of the error in redundant systems, the BER (or inversely the MTBF) may be twice the exponent or it may be no improvement if common to both. 

The specified BER establishes the channel reliability needs or the integrity of the data.  These are often define as soft errors that can be recovered with retries or correction or hard errors than cannot be corrected or recovered.  The spread of which can be several orders of magnitude.  It can also be rated by the time interval of tolerable retries for acceptable performance.

Retries in transmission systems, may be trivial and even transparent to the user in operating systems {e.g. Windows [win]+R >  cmd > netstat -es} Whereas avoid the error may be costly to reserve time to avoid contention or add more immunity from EMI from infrequent motor shutoff switch arc disturbances.

There are many statistical relationships between BER and other factors that affect cost, bit rate and bandwidth. Factors which  lower BER include environmental stress, aging, noise types, , quality margin loss, but can be improved by coding methods, modulation type, detection method, forward error detection/correction methods, and retry methods.  

Each tends to have logarithmic effects on BER equivalent to some noise in addition to the random Gaussian noise defined by the Shannon-Hartley equation \$ C=B ~log_2(1+S/N)~~~\$ and Shannon's Law for Channel capacity, C and Bandwidth, B for power in watts of Signal and Noise. This leads to the general shape and  slope of the BER curve vs number of bits with including all other factors that influence it.

BER Optimization tradeoffs include; 

MAXimize transmission bit rate
MAXimize system utilization
Minimize system complexity
Minimize transmission power
Minimize required system bandwidth, B
Optimize costs
Choose optimal modulation for  efficiency of B vs Tx Pwr
Choose optimal modulation due to disturbances, fading loss etc.


Minimize probability of bit error


  It all depends on the cost impact of an error vs the cost of retransmission, or overhead of error correction or the cost of each of the above factors, but specifications can be justified for many exponential powers of 10.


I could (probably) write a book on all my experiences with BER vs "any factor" measured by dB or ns jitter or costs to "margin of error" but I have been lucky to have lots of wide exposure to this topic. From 10 yrs experience in testing HDD Disk Drives during the 80-90's but BER was often defined as soft BER  \$ 10^{-10} \$ and hard BER \$ 10^{-14} \$ and originally did not include error correction so analog mapping of defects in the factory was critical.   But still in a SATA drive hard BER \$ 10^{-14} = \$ 8% per terabyte.  Thus the error correction methods with associated overhead and quality of media had to be improved with capacity.  The down-side is that "transparency" and lack of user awareness from automated error correction means the thresholds all appear to be compressed and the user never  gets any warning from working perfect one day to  failed permanently the next day.

BTW "can correct BER upto 10^(-3)" meant the correction method works from 1 bit per thousand and up.

In WiFi networks when the error rate exceeds a hard coded threshold, the bit rate negotiates to a lower rate. The Rx power level associated with this can vary from -80dBm to -60dBm with rising bit rates but can also be adversely affected by Rician Fading loss from phase cancelling echoes and drop the bit rates abruptly.