Recursive maximum-likelihood decoding algorithm for binary linear block codes

This paper presents a recursive maximum likelihood decoding algorithm for binary linear block codes based on a divide-and-conquer technique. A code is first divided into sections of short lengths. The distinct vectors in each section is partitioned into cosets of a linear block code. For each section, a metric table is formed, which stores the largest metric of each coset and the vector with the largest metric. These metric tables are then combined into metric tables for longer sections. The combination is carried out recursively until the full length of the code is reached. At this point, there is only one metric table which contains only the most likely codeword and its metric. To implement the combination of metric tables, the trellis structure of the code is used. A special one-section trellis is used for each combination of two metric tables. The overall trellis complexity of all the one-section trellises is much smaller than the full trellis of the code. As a result, this recursive maximum likelihood decoding algorithm is much simpler and more efficient than the Viterbi decoding algorithm. Furthermore, the algorithm allows parallel/pipeline processing of received words. Metric tables at each recursion level can be formed simultaneously in parallel and different received words can be processed in pipeline. This speeds up the decoding process. A decoder for a (64,40,8) Reed-Muller subcode operating at 600 Mbs (information bits) is being designed.