A Trellis Error Modeling Approach to Decoding Distributed Turbo Codes

In this paper, we re-examine the decoding problem of a distributed turbo code (DTC) over the three-node one-way relay channel based on the decode-and-forward protocol. In the traditional DTC scheme, the decoder at the destination assumes the error-free Viterbi decoding at the relay. However, the error propagation effect resulting from unsuccessful decoding at the relay may cause significant performance loss in some practical scenarios. Improved decoders reported in the literature typically assume a certain memoryless error model, which ignores the fact that relay decoding errors are correlated and bursty. In this paper, we propose a novel trellis error model (TEM) to accurately represent the statistics of relay decoding errors and construct two TEM-based iterative decoders (TEM-IDs) with two and three components, respectively. The TEM-ID with three components has a lower complexity than that of the TEM-ID with two components at the cost of minor performance loss. We also derive a new BER bound for the near maximum likelihood decoding of the DTC using a uniform interleaver. In addition, the extrinsic information transfer chart analysis is applied to estimate the threshold performance of the TEM-ID for large code lengths. Extensive simulation results verify that the new decoders can perform close to the derived BER bound and outperform existing decoders. Finally, we show that the TEM-ID can be extended for general distributed concatenated coding systems.