Bit-error rate performance of the (63,57) Hamming code and a severely punctured convolution code with maximum likelihood decoding

Severely punctured codes derived from the constraint length seven, rate-1/2 convolutional code are considered. By severely punctured the authors mean that the entire output of one of the two encoding parity circuits is deleted and the only redundancy in the transmission is conveyed in the code tail. It is seen that severely punctured codes are nonsystematic high-rate block codes; in one case, the (63,57) Hamming code results. The performance of severely punctured codes and the equivalent systematic codes is obtained assuming maximum likelihood decoding. It is shown that when post-decoding bit-error rate is used as the figure of merit, the systematic codes perform somewhat better. Straight-forward modifications to the standard Viterbi decoder for convolutional codes are identified which enable decoding of both the severely punctured codes and the equivalent systematic codes. As a consequence, it is seen that the Viterbi decoder for the K=7 nonsystematic convolutional code can be used to decode the systematic (63,57) Hamming code