A recursive Hadamard transform optimal soft decision decoding algorithm

A recursive soft decision maximum likelihood Hadamard transform decoding rule for binary code is derived. This algorithm, with computational complexity that varies inversely with the code rate for a fixed code length, is efficiently applicable for decoding convolutional codes and high rate block codes. An even more significant reduction in decoder complexity is obtained when the algorithm is applied for decoding product codes and concatenated codes. This algorithm achieves the computational efficiency of the Viterbi algorithm. In addition, its structural regularity simplifies the VLSI implementation of decoders.