Analysis of Relay Channels and Improved Iterative Decoders for Turbo-Coded Decode-and-Forward Relay Channels

Abstract: Three-node relay channels which consist of a source, a relay and a destination are considered in this thesis. In the first part, an uncoded relay channel is studied. The maximum likelihood (ML) detection rule for the detectand- forward relaying in additive white Gaussian noise (AWGN) channels which takes into account the detecting errors at the relay is formulated. Based on this rule, the upper bound on the probability of error at the destination’s receiver is analyzed. The source-relay-destination channel is assumed to be equivalent to an AWGN channel with an equivalent signalto- noise ratio (SNR) γeq. For the first time, the γeq is analyzed and its exact analytical expression is derived. In the second part, a more sophisticated relay channel called the turbocoded decode-and-forward relay channel is considered. Two recursive systematic convolutional (RSC) codes are implemented at the source and the relay which form a turbo-like encoding scheme. An improved maximum a posteriori decoder (IMAPD) which takes into account the decoding errors at the relay is analyzed. This decoder is implemented in an iterative manner similar to the traditional iterative decoder used for turbo codes. The performance of this IMAPD is compared with the performance of an iterative decoder commonly used in the literature which does not take into account the decoding errors at the relay, by simulation. The comparison shows that although the proposed IMAPD provides a better performance, especially when many decoding errors occur at the relay, the improvement is not significant. Then, another heuristical modification for the iterative decoder is proposed. In spite of the lack of theoretical analysis, the numerical results show that the proposed heuristically modified iterative decoder (HMID) gives significantly better performance than the traditional one.