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Title: Design of LDPC codes and reliable practical decoders for standard and non-standard channels
Keywords: LDPC codes, non-binary codes, pseudocodewords, log-likelihood ratios, differential PSK, pilot-symbol-assisted transmission
Issue Date: 22-Dec-2009
Citation: MO HUISI, ELISA (2009-12-22). Design of LDPC codes and reliable practical decoders for standard and non-standard channels. ScholarBank@NUS Repository.
Abstract: Low-density parity-check (LDPC) codes are known for their near Shannon-limit performance. Since non-binary LDPC codes are generally capable of outperforming binary LDPC codes, much interest were involved in the construction of good non-binary codes. However, decoding complexity increases with the alphabet size. Following recent work on mixed-alphabet codes, we design near-regular LDPC codes where the information symbols and majority of the parity-check symbols are defined over an integer residue ring, while the remaining parity-check symbols are defined over another integer residue ring of a larger size. Further, it has been shown that performance of the iterative decoder improves when redundant check nodes are added to the Tanner graph. This motivates our research on structured LDPC codes over integer residue rings, where the corresponding Tanner graphs with constant variable and check node degrees contain redundant check nodes. The original decoding algorithm proposed by Gallager is designed for transmission over the additive white Gaussian noise channel. Since then, performance of LDPC codes transmitted using modulation other than the binary phase shift keying (BPSK) over other types of channels was investigated. However, the decoding algorithm, the computation of the log-likelihood ratios (LLRs) in particular, is either executed with assumptions on the channel or altered based on unnecessary approximations. The calculation of the LLR is revisited and the optimal LLR for LDPC codes transmitted using binary differential PSK (BDPSK) over the noncoherent channel is derived. The computation is further generalized to the case with quadrature DPSK (QDPSK) and performances of binary as well as mixed-alphabet LDPC codes over the noncoherent channel are examined. We analyse finite-length binary and mixed-alphabet LDPC codes under BDPSK and QDPSK, and explain the difference in error performance under these two transmissions using the notion of pseudocodewords. Further, wederive the LLR for pilot-symbol-assisted BPSK transmission which yields better performance than BDPSK transmission but requires higher bandwidth. Extension to higher order modulations and non-binary codes shall be left for possible future research.
Appears in Collections:Ph.D Theses (Open)

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