Capacity-approaching coding schemes based on low-density parity-check codes

This dissertation proposes some coding schemes based on low-density parity-check (LDPC) codes. We demonstrate that these schemes can approach the channel capacity if the LDPC component codes are properly designed. We first consider the performance evaluation of LDPC codes on a binary-input Rayleigh fading channel, which is an important channel model for wireless communications. We extend the decoding analysis of LDPC codes to such a channel and address two important properties related to the convergence of the analysis. The performance of the optimized LDPC codes is very close to the capacity of this channel. We then design bandwidth-efficient multi-level coding (MLC) and bit-interleaved coded modulation (BICM) schemes based on LDPC codes. To make the performance analysis feasible, we introduce two different approaches: one based on independent identically distributed (i.i.d.) channel adapters and the other based on coset codes. We jointly optimize the component code rates and code parameters of the LDPC codes for the MLC scheme, and the optimized LDPC codes at each level of MLC achieve reliable transmission at signal-to-noise ratios (SNR) very close to the capacity of the additive white Gaussian noise (AWGN) channel. We demonstrate that the optimized LDPC-coded BICM scheme can perform well close to the capacity as well. We also compare the simulated performance of these schemes at moderate blocksizes, and consider the results from the perspective of random coding exponent analysis. Finally, we consider a high data rate system utilizing multiple antennas at both the transmitter and receiver where LDPC codes are used as channel codes. We employ an iterative receiver structure where soft information is exchanged iteratively between the demapper/detector and the decoder. Extrinsic information transfer (EXIT) charts analysis is applied to study the convergence behavior of the iterative decoding schemes. We introduce a novel code optimization method based on EXIT chart analysis, and a resulting rate-1/2 LDPC code achieves reliable transmission within 0.15dB of the capacity of a 2-input 2-output Rayleigh fading channel with 4-PAM signaling. To simplify the LDPC code design, we also propose to modify the coding scheme by using a space-time block code as an inner code.