A comparison of adaptive belief propagation and the best graph algorithm for the decoding of linear block codes

In this paper, two iterative message passing algorithms based on belief propagation proposed for the decoding of any binary linear block code are compared. The innovation of these algorithms lies in the fact that the structure of the graph of the parity check matrix is adaptively modified to render it suitable to belief propagation decoding. The modification is done such that the least reliable bits received from the channel are leaves of the graph. These algorithms perform favorably when compared with existing hard and iterative soft decision decoding algorithms in terms of error rate while maintaining a complexity polynomial in block length. It was found that while these two algorithms are conceptually similar, their performance in terms of word error rate (as a function of signal-to-noise ratio), decoding time (average number of iterations) and the updated bit reliabilities are very different