Research On Iterative Soft-Decision Decoding Of LDPC And GLD Codes

Efficient channel error-correction techniques are much necessary for various existing systems, such as advanced mobile communications, optical communications, and magnetic recording systems. Low-density parity-check (LDPC) and generalized low-density (GLD) codes have been attracting a great deal of research interest, due to their good capacity-approaching decoding performance. In this thesis, we mainly discuss the iterative soft-decision decoding of LDPC and GLD codes. We design two efficient iterative decoding algorithms named conditioned BP (belief propagation) and Chase-MP (message passing) algorithms, and also present several improved methods for analyzing the performance of BP decoding, and for designing the BP-based algorithms. Precisely, our work can be divided into the following four parts.1. Present the conditioned BP algorithm for decoding LDPC codes: We deduce the magnitude inequality on the Tanh rule, and conclude that the upper and inferior bounds of the inequality are tight or approximately tight in a certain condition. Based on the inequality and its corollaries, we design the conditioned BP algorithm, which can provide a good trade-off between the decoding performance and computational complexity. On the BI-AWGN (binary-input additive white Gaussian noise) channel, plenty of experimental simulations for regular and near-regular LDPC codes show that the conditioned BP algorithm is efficient.2. Present the EXIT (extrinsic information transfer)-trajectory and EXIT-equation methods for the performance analysis of BP decoding of LDPC codes: By improving the utility of EXIT analysis of BP decoding on the BI-AWGN channel, we present the EXIT-trajectory method, and extend it to the case of BI-Rayleigh fading channel; the EXIT-equation method makes use of the equation derived from EXIT functions, by which the problem of finding the convergence threshold for a given regular or irregular LDPC code can be described as a minimizing optimization. Numerical calculations on the decoding thresholds show the validity of these two designed EXIT methods.3. Present the EXIT-based and improve the MMSE (minimum mean square error)-based optimization of designing the scaled/offset BP-based algorithms for decoding LDPC codes: For short LDPC codes, we deduce the optimum scale/offset factors of these two BP-based algorithms by using the MMSE criterion; for LDPC codes with moderate lengths, we present the EXIT-trajectory method for determining these two optimum factors by using the EXIT analysis. On the channels of BI-AWGN and Rayleigh fading, we give the numerical results on the optimum factors, and the experimental simulations demonstrate that these two designing methods are valid.4. Present the Chase-MP iterative decoding algorithm for GLD codes, and provide the performance analysis of the iterative algorithm by using the Gaussian approximation on the BI-AWGN channel: We give a fast hybrid method for the realization of Chase-II decoding, by which the low-complexity Chase-MP algorithm is designed based on the Tanner graph of the low-density matrix. By using...