Analytical Expressions Used in
bercoding Function and Bit
Error Rate Analysis App
This table describes the additional notations used in analytical expressions in this section.
|Energy-per-information bit-to-noise power-spectral-density ratio|
This section describes the specific notation for block coding expressions, where is the minimum distance of the code.
For BPSK, QPSK, OQPSK, 2-PAM, 4-QAM, and precoded MSK, equation 8.1-52 in ) applies,
For DE-BPSK, DE-QPSK, DE-OQPSK, and DE-MSK,
For BFSK coherent detection, equations 8.1-50 and 8.1-58 in  apply,
For BFSK noncoherent square-law detection, equations 8.1-65 and 8.1-64 in  apply,
where is the average number of channel symbol errors that remain in corrected N-tuple format when the channel caused m symbol errors (see table 4.2 in ).
For Reed-Solomon code with ,
otherwise, if , where h is an integer (equation 1 in ) applies,
where s is the SER in an uncoded AWGN channel.
For example, for BPSK, and , otherwise is given by table 1 and equation 2 in .
This section describes the specific notation for convolutional coding expressions, where is the free distance of the code, and is the number of paths of distance d from the all-zero path that merges with the all-zero path for the first time.
The transfer function is given by
where is the exponent of N as a function of d.
This equation gives the results for BPSK, QPSK, OQPSK, 2-PAM, 4-QAM, precoded MSK, DE-BPSK, DE-QPSK, DE-OQPSK, DE-MSK, DPSK, and BFSK:
where is the BER in the corresponding uncoded AWGN channel. For example, for BPSK (equation 8.2-20 in ),
When d is odd,
and when d is even,
where p is the bit error rate (BER) in an uncoded AWGN channel.