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한국통신학회논문지

Design and Implementation of a High-Reliability Min-Max Algorithm for LDPC Decoder on FPGA

Heung-Ryol Yoo, Yung-Deug Son

Published Dec 23, 2024• 0 citations
Publisher

Abstract

LDPC codes improve error correction performance in soft-decision decoding by using the reliability of the received signal, offering greater accuracy than hard-decision decoding. The High Reliability Min-Max Algorithm leverages this advantage by using LLR to reduce computational complexity while improving decoding accuracy. The (837, 726) Min-Max code maintains performance similar to LDPC while being more efficient, reducing hardware resource usage and power consumption. Compared to the (4191, 3602) binary LDPC code, it offers better transmission efficiency. This paper presents the simulation results for a (512, 256) code, and the hardware implementation, using pipeline and parallel structures, highlights the high error correction capability of the proposed Min-Max code. This structure combines the error correction strengths of QC-LDPC with the simplicity of binary LDPC's hardware implementation. The proposed algorithm demonstrates similar error correction performance to LDPC codes but achieves lower complexity and higher transmission efficiency. Future research will focus on comparing the performance through ASIC implementation to further assess its effectiveness in practical systems. This comparison will offer insights into how the proposed Min-Max code can be implemented for real-world applications requiring efficient and reliable error correction performance.

DOI
10.7840/kics.2024.49.12.1792

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LDPC codes improve error correction performance in soft-decision decoding by using the reliability of the received signal, offering greater accuracy than hard-decision decoding. The High Reliability Min-Max Algorithm leverages this advantage by using LLR to reduce computational complexity while improving decoding accuracy. The (837, 726) Min-Max code maintains performance similar to LDPC while being more efficient, reducing hardware resource usage and power consumption. Compared to the (4191, 3602) binary LDPC code, it offers better transmission efficiency. This paper presents the simulation results for a (512, 256) code, and the hardware implementation, using pipeline and parallel structures, highlights the high error correction capability of the proposed Min-Max code. This structure combines the error correction strengths of QC-LDPC with the simplicity of binary LDPC's hardware implementation. The proposed algorithm demonstrates similar error correction performance to LDPC codes but achieves lower complexity and higher transmission efficiency. Future research will focus on comparing the performance through ASIC implementation to further assess its effectiveness in practical systems. This comparison will offer insights into how the proposed Min-Max code can be implemented for real-world applications requiring efficient and reliable error correction performance.
This thesis is focused on the design and implementation of binary low-density parity-check (LDPC) code decoders for high-speed modern communication systems. The basic of LDPC codes and the performance and bottlenecks, in terms of complexity and hardware efficiency, of the main soft-decision and hard-decision decoding algorithms (such as Min-Sum, Optimized 2-bit Min-Sum and Reliability-based iterative Majority-Logic) are analyzed. The complexity and performance of those algorithms are improved to allow efficient hardware architectures.\n\nA new decoding algorithm called One-Minimum Min-Sum is proposed. It reduces considerably the complexity of the check node update equations of the Min-Sum algorithm. The second minimum is estimated from the first minimum value by a means of a linear approximation that allows a dynamic adjustment. The Optimized 2-bit Min-Sum algorithm is modified to initialize it with the complete LLR values and to introduce the extrinsic information in the messages sent from the variable nodes. Its variable node equation is reformulated to reduce its complexity. Both algorithms were tested for the (2048,1723) RS-based LDPC code and (16129,15372) LDPC code using an FPGA-based hardware emulator. They exhibit BER performance very close to Min-Sum algorithm and do not introduce early error-floor. \n\nIn order to show the hardware advantages of the proposed algorithms, hardware decoders were implemented in a 90 nm CMOS process and FPGA devices based on two types of architectures: full-parallel and partial-parallel one with horizontal layered schedule. The results show that the decoders are more area-time efficient than other published decoders and that the low-complexity of the Modified Optimized 2-bit Min-Sum allows the implementation of 10 Gbps decoders in current FPGA devices. \n\nFinally, a new hard-decision decoding algorithm, the Historical-Extrinsic Reliability-Based Iterative Decoder, is presented. This algorithm introduces the new idea of considering hard-decision votes as soft-decision to compute the extrinsic information of previous iterations. It is suitable for high-rate codes and improves the BER performance of the previous RBI-MLGD algorithms, with similar complexity.
Error Correction Codes (ECCs) stand as a linchpin in ensuring data accuracy in wireless communication.As the landscape of modern communication standards continues to expand, there is a mounting inclination towards efficient ECC technologies, such as Low-Density Parity-Check codes (LDPCs).Distinguished by their near-capacity performance and low computational complexity, LDPCs are increasingly utilized in the successful encoding and decoding of data.This study undertakes an exploration of recent advancements in LDPC research, encompassing the analysis of decoding algorithms, architectures, applications, simulations, real-world implementations, and complexities across various hardware platforms.The central research problem addressed within this work is the identification of the most efficacious LDPC decoder implementation, with an emphasis placed on Field-Programmable Gate Array (FPGA) technology.From the outcomes of this study, the Min-Sum algorithm emerged as the favored choice for LDPC decoding, particularly within FPGA implementations.The selection of this algorithm is attributable to its simplicity and implementation feasibility, thus directly addressing the posed research problem.The inherent simplicity of the Min-Sum algorithm's structure renders it a practical choice for real-world applications.Further, its proficiency in error correction and compatibility with FPGA hardware underscore its potential for augmenting the reliability of data transmission in communication systems.The findings of this study advocate for the Min-Sum algorithm as a valuable asset in LDPC decoding, notably within FPGA implementations.This positions it as a promising candidate for optimizing data communication systems.The selection of FPGA as the implementation platform reaffirms its practicality and relevance in contemporary communication technology, thus offering a comprehensive solution to the identified research problem.
Binary Low-Density Parity-Check (LDPC) codes are a type of error correction code known to exhibit excellent error-correcting capabilities, and have increasingly been applied as the forward error correction solution in a multitude of systems and standards, such as wireless communications, wireline communications, and data storage systems. In the pursuit of codes with even higher coding gain, non-binary LDPC (NB-LDPC) codes defined over a Galois field of order q have risen as a strong replacement candidate. For codes defined with similar rate and length, NB-LDPC codes exhibit a significant coding gain improvement relative to that of their binary counterparts.Unfortunately, NB-LDPC codes are currently limited from practical application by the immense complexity of their decoding algorithms, because the improved error-rate performance of higher field orders comes at the cost of increasing decoding algorithm complexity. Currently available ASIC implementation solutions for NB-LDPC code decoders are simultaneously low in throughput and power-hungry, leading to a low energy efficiency.We propose several techniques at the algorithm level as well as hardware architecture level in an attempt to bring NB-LDPC codes closer to practical deployment. On the algorithm side, we propose several algorithmic modifications and analyze the corresponding hardware cost alleviation as well as impact on coding gain. We also study the quantization scheme for NB-LDPC decoders, again in the context of both the hardware and coding gain impacts, and we propose a technique that enables a good tradeoff in this space. On the hardware side, we develop a FPGA-based NB-LDPC decoder platform for architecture prototyping as well as hardware acceleration of code evaluation via error rate simulations. We also discuss the architectural techniques and innovations corresponding to our proposed algorithm for optimization of the implementation. Finally, a proof-of-concept ASIC chip is realized that integrates many of the proposed techniques. We are able to achieve a 3.7x improvement in the information throughput and 23.8x improvement in the energy efficiency over prior state-of-the-art, without sacrificing the strong error correcting capabilities of the NB-LDPC code.
When the code length is moderate, non-binary low-density parity-check (NB-LDPC) codes can achieve better error correcting performance than their binary counterparts at the expense of higher decoding complexity. The check node processing is a major bottleneck of NB-LDPC decoding. In this paper, Min-max decoding algorithm is proposed based on a new forward backward processing method of check nodes, select only a part of the most reliable information to the forward-backward calculation process, and change the variable nodes to check nodes (v-to-c) generation of information. Using this algorithm, a kind of code (768,1152) defined on GF(4) is simulated and compared with belief propagation in log domain (LOG-BP) decoding algorithm. Simulation results show Min-max decoding algorithm reduce information storage requirements and the computational complexity, conducive to engineering implementation.
Compared to binary Low-Density Parity-Check (LDPC) codes, nonbinary LDPC (NB-LDPC) codes have better error correction performance under short-to-moderate block lengths or high-order modulations. Traditional min-sum-based soft decoding algorithms for NB-LDPC codes suffer from large computational complexity, which leads to inefficient hardware implementations. The Multiple-symbol-reliability weighted Bit-Reliability-Based (MwBRB) hard decoding algorithm achieves a good tradeoff between error correction performance and decoding complexity. However, efficient hardware implementations based on the MwBRB algorithm have not been investigated. In this brief, an improved layered MwBRB algorithm is first proposed, which results in faster convergence rate than the MwBRB algorithm. Then, an ultra-high-throughput low-complexity decoder architecture with an efficient partially parallel processing schedule is also presented. Finally, the proposed architecture is coded with RTL and synthesized under the TSMC 90-nm CMOS technology. The synthesis results demonstrate that the proposed decoder for a (837, 726) quasi-cyclic NB-LDPC code over GF(25) achieves a throughput of 21.66 Gbps and an area efficiency of 4.77 Gbps/M-gates under the TSMC 90-nm CMOS technology. The proposed decoder reaches a throughput more than 20 Gbps for the first time among the prior NB-LDPC decoders, and the area efficiency is far beyond the state-of-the-art designs.