Research On Decoder For LDPC Codes Via Penalty Dual Decomposition Method

Low density parity check(LDPC)codes have been widely used in various communication tasks due to their excellent performance approaching to Shannon capacity limits.Besides the classical belief propagation(BP)algorithm,the linear programming(LP)decoding algorithm based on maximum likelihood(ML)has drawn significant attention from worldwide researchers due to its strong theoretical guarantee and excellent performance.How to reduce the high complexity of LP decoding and further improve the decoding performance has become a research hotspot in recent years.The penalty dual decomposition(PDD)algorithm is suitable for solving large-scale distributed optimization problems.In this thesis,we solve the LP decoding problem of LDPC codes based on the PDD framework,and employ the deep unfolding technology to improve the performance of the decoder.Besides,the idea of LP decoding is extended to the LDPC decoding problem under the inter-symbol interference(ISI)channel.Firstly,we introduce the theoretical basis of LDPC codes and classical BP decoding algorithms,and then describe the basic principles of Turbo equalization based on the ISI channel.Besides,we introduce the PDD framework,and summarize the existing deep learning technologis.In particular,we introduce the deep unfolding technique based on model-driven deep learning.Secondly,we develop a double-loop iterative PDD decoding algorithm based on LP decoding of LDPC codes.Specifically,we first introduce the cascaded integer programming problem of the ML decoding,and utlize the LP relaxation to handle the discrete constraints and the penalty method to avoid pseudocodewords.Then,We propose the PDD decoding algorithm based on the cascaded integer programming problem and employ the over-relaxation method to improve convergence.Besides,to avoid manually finetuning the decoding parameters and to further improve the decoding performance,we unfold the proposed PDD decoding algorithm into a model-driven neural network,namely the learnable PDD decoding network(LPDN).We turn the tunable coefficients and parameters in the proposed PDD decoder into layer-dependent trainable parameters which can be optimized by gradient descent-based methods during network training.Simulation results demonstrate that the proposed LPDN with well-trained parameters is able to provide superior error-correction performance with much lower computational complexity as compared to the PDD decoder.Finally,we extend the idea of LP decoding to ISI channel,and propose a PDD decoding algorithm for LDPC codes over ISI channel.Specifically,we first formulate the ML decoding for the LDPC codes over ISI channel as a Quadratic Programming(QP)problem,and utilize the LP relaxation and the penalty method to simplify the constraints.Then,we propose the ISI-PDD decoding algorithm based on check polytope constraints.Besides,to reduce the projection step of check polytope in the decoding algorithm,we propose an iterative fast check polytope projection(FCPP)algorithm,in which an adjustable scaling factor is introduced to improve convergence.Simulation results demonstrate that FCPP can reduce the iteration number of the projection algorithm without degrading the decoding performance.Besides,we show that the proposed PDD decoding algorithm based on ISI channel has better error-correction performance than the classical Turbo equalization decoding,and its computational complexity increases linearly with the memory length of ISI channel.