Mathematics, Department of


Date of this Version



Published in 2008 5th International Symposium on Turbo Codes and Related Topics

doi 10.1109/TURBOCODING.2008.4658725


Copyright 2008 IEEE. Used by permission.


Simulations have shown that the outputs of minsum (MS) decoding generally behave in one of two ways: the output either eventually stabilizes at a codeword or eventually cycles through a finite set of vectors that may include both codewords and non-codewords. This inconsistency in MS across iterations has significantly contributed to the difficulty in studying the performance of this decoder. To overcome this problem, a new decoder, average min-sum (AMS), is proposed; this decoder outputs the average of the min-sum output vectors over a finite set of iterations. Simulations comparing MS, AMS, linear programming (LP) decoding, and maximum likelihood (ML) decoding are presented, illustrating the relative performances of each of these decoders. In general, MS and AMS have comparable word error rates, and in the simulation most resembling codes of practical interest AMS is shown to have significantly lower bit error rate, demonstrating the potential benefits of this decoder in its own right. Additionally, the performance of MS and AMS relative to ML and LP decoding is consistent across simulations, indicating that AMS is a valid and potentially important tool for better analyzing MS performance and its relationship to other decoders. Finally, AMS pseudocodewords are introduced and analyzed and their relationship to graph cover and LP pseudocodewords is explored, with particular focus on the AMS pseudocodewords of regular LDPC codes and cycle codes.