Stack Decoding of Linear Block Codes for Discrete Memoryless Channel Using Tree Diagram

The boundaries between block and convolutional codes have become diffused after recent advances in the understanding of the trellis structure of block codes and the tail-biting structure of some convolutional codes. Therefore, decoding algorithms traditionally proposed for decoding convolutional codes have been applied for decoding certain classes of block codes. This paper presents the decoding of block codes using tree structure. Many good block codes are presently known. Several of them have been used in applications ranging from deep space communication to error control in storage systems. But the primary difficulty with applying Viterbi or BCJR algorithms to decode of block codes is that, even though they are optimum decoding methods, the promised bit error rates are not achieved in practice at data rates close to capacity. This is because the decoding effort is fixed and grows with block length, and thus only short block length codes can be used. Therefore, an important practical question is whether a suboptimal realizable soft decision decoding method can be found for block codes. A noteworthy result which provides a partial answer to this question is described in the following sections. This result of near optimum decoding will be used as motivation for the investigation of different soft decision decoding methods for linear block codes which can lead to the development of efficient decoding algorithms. The code tree can be treated as an expanded version of the trellis, where every path is totally distinct from every other path. We have derived the tree structure for (8, 4) and (16, 11) extended Hamming codes and have succeeded in implementing the soft decision stack algorithm to decode them. For the discrete memoryless channel, gains in excess of 1.5dB at a bit error rate of 10-5 with respect to conventional hard decision decoding are demonstrated for these codes.