Low complexity channel coding and asymptotics of Viterbi encoded trellis coded quantization.

摘要

In this thesis, we propose a new class of channel coding schemes and investigate their applications to Additive White Gaussian Noise (AWGN) channels and Partial Response (PR) channels. We also study the asymptotics of the Viterbi encoded Trellis Coded Quantization (TCQ).; This thesis develops a class of application-oriented channel coding schemes, which include concatenated or non-concatenated specially designed Recursive Systematic Ordinary Convolutional (RSOC) codes. A simplified symbol-by-symbol maximum a posteriori (MAP) algorithm is derived to decode the RSOC codes, which works on the trellises of the reciprocal dual codes of the RSOC codes. The proposed decoding algorithm is intrinsically partial parallel and can be further paralleled without performance loss.; Over AWGN channels, compared with the well-known turbo codes and Low Density Parity Check (LDPC) codes, the proposed coding schemes achieve better or similar Bit Error Rate (BER) and Block Error Rate (BLER) performance, while with considerably less overall complexity than the LDPC codes and turbo codes.; For the code applications in Lorentzian magnetic recording channels, we develop low complexity detection schemes with soft output based on estimation feedback. These detection schemes work quite well with the proposed codes, achieving comparable BER performance as more complicated systems that consist of MAP channel detectors, and LDPC codes or serial turbo codes.; We further investigate the error statistics of the proposed coding schemes over ideal PR channels and Lorentzian magnetic recording channels. The error statistics, i.e., the statistics of symbol errors in an incorrectly decoded codeword, are crucial for storage channels where outer Error Correction Codes (ECC) with certain error correction capability, usually Reed-Solomon codes, are used to achieve exceptionally high level of reliability. Our simulation results show that proposed coding schemes provide around 2 dB gains even measured after the outer ECC, compared with corresponding un-coded systems.; We also derive an algorithm based on Markov chain techniques to compute the exact Hamming distortion of Viterbi encoded TCQ on memoryless discrete random source. The optimal schemes of 2-state TCQ and 4-state TCQ are obtained with rate lbit/sample on uniformly distributed memoryless source of alphabet 4.