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arXiv:1605.04664

A Joint Optimization Technique for Multi-Edge Type LDPC Codes

Sachini Jayasooriya, Mahyar Shirvanimoghaddam, Lawrence Ong, Sarah J. Johnson

Published May 16, 2016• 0 citations
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Abstract

This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of MET-LDPC codes for given values of the maximum number of edge-types and maximum node degrees. This joint optimization is particularly important for MET-LDPC codes as it is not clear a priori which structures will be good. Using several examples, we demonstrate that the MET-LDPC codes designed by the proposed joint optimization algorithm exhibit improved decoding thresholds compared to previously reported MET-LDPC codes.

DOI
10.48550/arxiv.1605.04664

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This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of MET-LDPC codes for given values of the maximum number of edge-types and maximum node degrees. This joint optimization is particularly important for MET-LDPC codes as it is not clear a priori which structures will be good. Using several examples, we demonstrate that the MET-LDPC codes designed by the proposed joint optimization algorithm exhibit improved decoding thresholds compared to previously reported MET-LDPC codes.
This study considers the optimisation of multi‐edge type low‐density parity‐check (MET‐LDPC) codes to maximise the decoding threshold. The authors propose an algorithm to jointly optimise the node degree distribution and the multi‐edge structure of MET‐LDPC codes for given values of the maximum number of edge‐types and maximum node degrees. This joint optimisation is particularly important for MET‐LDPC codes as it is not clear a priori which structures will be good. Using several examples, they demonstrate that the MET‐LDPC codes designed by the proposed joint optimisation algorithm exhibit improved decoding thresholds compared with previously reported MET‐LDPC codes.
Designing multi-edge type low-density parity-check (MET-LDPC) code ensembles that satisfy structural constraints while achieving near-capacity performance remains a challenging problem. Existing methods, including those based on differential evolution, have improved flexibility but still face limitations such as high computational cost and the need for manual configuration of edge patterns. We propose an optimization-based method that explores diverse, structurally feasible edge distribution candidates and optimizes node distributions via a constrained linear system formulation. A dual annealing optimizer is then applied to identify node profiles that maximize the decoding threshold. Evaluations on both the binary erasure channel and the binary-input additive white Gaussian noise channel across multiple code rates show that our method consistently produces ensembles with strong threshold performance and low edge complexity, highlighting its practicality and adaptability.
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This paper considers density evolution for low-density parity-check (LDPC) and multi-edge type LDPC (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three single-parameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely, at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus, single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared with full density evolution thereby making it more suitable for code design.
A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief propagation, passes messages along the edges of this Tanner graph. Density evolution is an efficient method to analyze the performance of the belief propagation decoding algorithm for a particular LDPC code ensemble, enabling the determination of a decoding threshold. The basic problem addressed in this work is how to optimize the Tanner graph so that the decoding threshold is as large as possible. We introduce a new code optimization technique which involves the search space range which can be thought of as minimizing randomness in differential evolution or limiting the search range in exhaustive search. This technique is applied to the design of good irregular LDPC codes and multi-edge type LDPC codes.
In communication systems, the transmitted data is corrupted by channel perturbations, such as noise and fading, which affect the reliability of the received data. Error correction codes are employed to mitigate channel perturbations. However, design and implementation of good and efficient error correction codes remains an open problem. In this paper, Low Density Parity Check (LDPC) codes are considered as they provide a reasonable trade-off between computational complexity and reliability. Good LDPC codes should ideally provide low complexity, close to capacity acheivable transmission rate, high coding threshold, and high decoding stability. In this paper, we investigate a joint LDPC code optimization algorithm using Genetic Algorithm (GA) and Linear Programming (LP) to determine the variable nodes and check nodes degrees distributions. EXIT chart analysis and Frame Error Rate (FER) performance are used to validate the proposed method.