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IEEE Transactions on Consumer Electronics

Hardware efficient decoding of LDPC codes using partial-min algorithms

Jiabin Su, K. Liu, Hao Min

Published Nov 1, 2006• 6 citations
Publisher

Abstract

In this paper, the partial-min algorithms are proposed for updating the check node messages in decoding low-density parity-check (LDPC) codes. The proposed methods can achieve a good performance-versus-complexity tradeoff by reducing both the check node processor complexity and the decoder memory requirements. Float-point and fixed-point simulation results show that a near optimum performance can be maintained. The architecture of a check node processor implementing the partial-min algorithms is also presented. The hardware expense especially the memory requirement is analyzed and compared with normal decoding architectures

DOI
10.1109/tce.2006.273171

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In this paper, the partial-min algorithms are proposed for updating the check node messages in decoding low-density parity-check (LDPC) codes. The proposed methods can achieve a good performance-versus-complexity tradeoff by reducing both the check node processor complexity and the decoder memory requirements. Float-point and fixed-point simulation results show that a near optimum performance can be maintained. The architecture of a check node processor implementing the partial-min algorithms is also presented. The hardware expense especially the memory requirement is analyzed and compared with normal decoding architectures
This paper has presented various min-sum related LDPC decoding algorithms and their typical hardware architectures of check node update in the scenario of parallel implementation. The m-to-2m decoder has been introduced to generate more efficient new hardware implementations of check node update, which can obviously reduce the number of multiplication operations for normalized min-sum algorithm for high rate LDPC codes. Simulations have claimed the performance of normalized min-sum is nearly the same as that of Log-BP, namely the optimal algorithm. In general, this paper has proved that normalized min-sum is good choices as LDPC decoding methods.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
One of the most important units of Low-Density Parity-Check (LDPC) decoders is the Check-Node Unit.Its main task is to find the first two minimum values among incoming variable-to-check messages and return check-tovariable messages.This block significantly affects the decoding performance, as well as the hardware implementation complexity.In this paper, we first propose a modification to the check-node update rule by introducing two optimal offset factors applied to the check-to-variable messages.Then, we present the Check-Node Unit hardware architecture which performs the proposed algorithm.The main objective of this work aims to improve further the decoding performance for 5 th Generation (5G) LDPC codes.The simulation results show that the proposed algorithm achieves essential improvements in terms of error correction performance.More precisely, the error-floor does not appear within Bit-Error-Rate (BER) of 10 -8 , while the decoding gain increases up to 0.21 dB compared to the baseline Normalized Min-Sum, as well as several state-ofthe-art LDPC-based Min-Sum decoders.
This paper proposes a hardware-and memoryefficient architecture for Low-Density Parity-Check (LDPC) decoding, targeting enhanced-performance applications with constrained resources.The design integrates two novel techniques: (i) the Variable Single minimum Min-Sum (VSMS) algorithm, which reduces hardware complexity by identifying the first minimum value and its position during check node processing, while improving error correction through a correction factor applied in variable node updates; and (ii) a memory splitting strategy that exploits the structural properties of LDPC codes to optimize memory usage.Implementation on a Xilinx Kintex UltraScale+ (xcku5p) FPGA demonstrates a reduction in storage requirements by over 46.2% compared to conventional decoders.Furthermore, the proposed decoder achieves a performance gain of up to 0.38 dB at a Bit Error Rate (BER) of 10⁻⁸, outperforming traditional Min-Sum-based approaches.
Abstract: In this paper, a fast-convergence algorithm is proposed for the decoding of low-density parity-check (LDPC) codes. By putting more weight on the message update from check node to variable node in current iteration, the proposed method speeds up the decoding significantly. Simulation results show that compared with the standard layered min-sum decoding algorithm, the proposed scheme may reduce about 1/6 iteration numbers for LDPC codes used in DVB-S2, with hardware complexity overhead less than 2%. Key–Words: LDPC code, fast convergence decoding algorithm, layered decoding, min-sum algorithm, hardware implementation 1