Iterative decoding techniques for correlated Rayleigh fading and diversity channels

A novel channel coding scheme called turbo codes, or more precisely, parallel concatenated convolutional codes, is one of the most exciting channel coding schemes introduced in the last decade. The coding system is a novel combination of iterative decoding with soft-input/soft-output (SISO) algorithms and recursive systematic convolutional (RSC) codes in parallel connected by an interleaver. With these components, turbo codes can approach to the Shannon limit and perform very well in AWGN and independently fading channels. But their performance in correlated fading channels remains a question. Here we investigate turbo codes for correlated Rayleigh fading and then for diversity channels with combining techniques.; A particular SISO decoder, the BCJR decoding algorithm, is crucial for the success of turbo decoding. A special application of this algorithm, the tailbiting BCJR (TB-BCJR) decoder is implemented and compared to two different tailbiting decoders, namely the maximum likelihood (ML) and circular Viterbi algorithm decoders, in the BSC and AWGN channels. It is shown that the TB-BCJR performs as well as the ML decoder when the code length is relatively long.; At first, fading channels are modeled as erasure channels and turbo coding is applied to the BEC, several quantized AWGN channels with an erasure region and the Gilbert-Elliot channel models. The BUR algorithm is redesigned for erasure correction. Turbo decoding with this BUR decoder performs very well in the above erasure channels.; Then more realistic channel models which are encountered in cellular radio systems are constructed by using Jakes' fading simulator. By using this simulator, turbo coding is tested for correlated Rayleigh fading channels. Turbo codes are compared to simple convolutional codes. They outperform convolutional codes only after threshold blocklengths which are linearly dependent with fading bandwidths. These thresholds are unacceptably long in most practical radio systems. It is observed that lower complexity constituent encoders perform as well as more complex constituent encoders in these channels.; Employing diversity is an effective mitigation technique for correlated fading channels. We test diversity combining techniques with turbo decoding. Maximum ratio combining (MRC) and selective combining (SC) are implemented. The MRC is implemented in the turbo decoder as a post-detection and the SC as a pre-detection scheme. The MRC performs significantly better than the SC with turbo codes. Turbo decoding with diversity combining can achieve performances that can only be achieved by turbo codes with long blocks in a non-diversity system. Diversity combining increases the chance that turbo codes can be used in time critical applications where shorter delays are required.