Bit-error rate performance of the (63,57) Hamming code and aseverely punctured convolution code with maximum likelihooddecoding

摘要

Severely punctured codes derived from the constraint length seven,nrate-1/2 convolutional code are considered. By severely punctured thenauthors mean that the entire output of one of the two encoding parityncircuits is deleted and the only redundancy in the transmission isnconveyed in the code tail. It is seen that severely punctured codes arennonsystematic high-rate block codes; in one case, the (63,57) Hammingncode results. The performance of severely punctured codes and thenequivalent systematic codes is obtained assuming maximum likelihoodndecoding. It is shown that when post-decoding bit-error rate is used asnthe figure of merit, the systematic codes perform somewhat better.nStraight-forward modifications to the standard Viterbi decoder fornconvolutional codes are identified which enable decoding of both thenseverely punctured codes and the equivalent systematic codes. As anconsequence, it is seen that the Viterbi decoder for the K=7nnonsystematic convolutional code can be used to decode the systematicn(63,57) Hamming code