Maximum Likelihood Decoding of Turbo Codes on the Binary Erasure Channel

Abstract—In this paper we deal with Maximum Likelihood (ML) decoding of Turbo Codes on the Binary Erasure Channel. First we describe a new ML decoder. When the standard iterative decoder fails because the set of erasures includes a stopping set, with the component decoders we obtain a linear system of equations that seeks the codeword constrained by both component codes. We evaluate the complexity in terms of equivalent turbo iterations and we show that this ML decoder is implementable. We also modify the algorithm proposed in [6] for LDPC to decode Turbo Codes and we compare the two methods. We find that, in general, our method is more efficient with low memory or punctured codes. Finally, by simulation we show that m-ary Turbo Codes under ML decoding outperform the error exponent bounds for random codes down to WER=1e−6, for all rates ranging from 1/3 to 7/8.