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Informatyka Automatyka Pomiary w Gospodarce i Ochronie Środowiska

ITERATIVE DECODING OF SHORT LOW-DENSITY PARITY-CHECK CODES BASED ON DIFFERENTIAL EVOLUTION

Mykola Shtompel, С. И. Приходько

Published Jun 30, 2024• 1 citation
Publisher

Abstract

To ensure a given quality of service in the networks of the Internet of Things, short error-correcting codes are used, in particular, low-density parity-check codes. The paper proposes an approach for decoding these codes based on the joint application of belief propagation and differential evolution procedures. It is shown that in order to reduce the search area of error vectors based on differential evolution, it is necessary to use the least reliable basis of the parity-check matrix. Flowchart and pseudocode of the combined decoding algorithm of short low-density parity-check codes were presented. The simulation results showed that the proposed decoding method provides an additional gain from encoding compared to the classical decoding method. The application of the presented iterative decoding method of short low-density parity-check codes will improve the efficiency of data transmission in the infrastructure of the Internet of Things.

DOI
10.35784/iapgos.5762

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To ensure a given quality of service in the networks of the Internet of Things, short error-correcting codes are used, in particular, low-density parity-check codes. The paper proposes an approach for decoding these codes based on the joint application of belief propagation and differential evolution procedures. It is shown that in order to reduce the search area of error vectors based on differential evolution, it is necessary to use the least reliable basis of the parity-check matrix. Flowchart and pseudocode of the combined decoding algorithm of short low-density parity-check codes were presented. The simulation results showed that the proposed decoding method provides an additional gain from encoding compared to the classical decoding method. The application of the presented iterative decoding method of short low-density parity-check codes will improve the efficiency of data transmission in the infrastructure of the Internet of Things.
In this paper, an iterative soft-decision hybrid decoding algorithm for non-binary low-density parity-check (LDPC) codes with short codeword lengths is proposed. The rationale of the approach is to combine the classical belief propagation (BP) iterative LDPC decoding algorithm with the most reliable basis (MRB) decoding algorithm. This allows to achieve significant performance improvements, with a complexity that, for medium/low error rates, is only slightly higher than that of the BP algorithm alone. The performance improvement with respect to pure BP decoding is up to 0.7 dB at codeword error rate (CER) ≈ 10-5. Notably, for a fixed MRB order, hybrid decoding achieves a gain up to 0.5 dB at CER ≈ 10-5with respect to BP decoding and MRB decoding used alone.
In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated.
This paper proposes a two-stage iterative decoding scheme named matrix transform belief propagation scheme (MT-BP) based on conventional belief propagation (BP) algorithm for lowdensity parity-check (LDPC) codes.By introducing information measurement, location vectors and parity check matrix transform, the proposed method can establish additional parity check equations and take more information bits of variable nodes into consideration compared with conventional BP algorithm.The simulations are performed on random regular LDPC codes and algebraic quasi-cyclic codes (QC-LDPC), the experimental results show MT-BP method can efficiently reduce the bit error rate (BER).
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.
Low-density parity-check codes have recently received much attention because of their excellent performance and the availability of a simple iterative decoder. The decoder, however, requires large amounts of memory, which causes problems with memory consumption. We investigate a new decoding scheme for low density parity check codes to address this problem. The basic idea is to define a reliability measure and a threshold, and stop updating the messages for a bit whenever its reliability is higher than the threshold. We also consider some modifications to this scheme, including a dynamic threshold more suitable for codes with cycles, and a scheme with soft thresholds which allow the possibility of removing a decision which have proved wrong. By exploiting the bits different rates of convergence we are able to achieve an efficiency of up to 50% at a bit error rate of less than 10^-5. The efficiency should roughly correspond to the power consumption of a hardware implementation of the algorithm.
An improved belief propagation(BP) decoding scheme was put forward to solve the high complexity and low decoding efficiency problem of BP in low density parity check(LDPC) codes.Because different bit nodes and check nodes have different reliability and contribute differently to BP decoding;the proposed decoding scheme employs a differentiate rule based on lawless check number and pseudo posterior probability to evaluate every bit's reliability before each step of iteration;The nodes have little lawless check number and large pseudo posterior probability are supposed to have higher reliability.The bits with high reliability need not to be updated by the decoder.Simulation shows that the proposed BP decoding algorithm can reduce the computational load and increase the decoding efficiency significantly.