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Signal Processing and Communications Applications Conference (SIU)

High Performance and Resource Efficient Low Density Parity Check Decoder Design

Burak Ünal

Published Jun 25, 2025• 0 citations
Publisher

Abstract

Low Density Parity Check (LDPC) codes have gained popularity in communication systems due to their capacity-approaching error correction performance. In this study, a high-performance LDPC decoding algorithm with extremely low resource usage is proposed. Among the hard decision class of LDPC decoders, Gallager B (GaB) provides high-performance hardware due to its computational simplicity. However, GaB suffers from poor error-correction performance. In this study, a new intrinsic computation technique for GaB called Intrinsic Gallager B (IGaB) is introduced to improve error correction performance. Our simulation results show that the IGaB algorithm provides better error correction performance compared with GaB. GaB and IGaB algorithms are implemented on Field Programmable Gate Array (FPGA) to compare hardware performance.

DOI
10.1109/siu66497.2025.11112140

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Low Density Parity Check (LDPC) codes have gained popularity in communication systems due to their capacity-approaching error correction performance. In this study, a high-performance LDPC decoding algorithm with extremely low resource usage is proposed. Among the hard decision class of LDPC decoders, Gallager B (GaB) provides high-performance hardware due to its computational simplicity. However, GaB suffers from poor error-correction performance. In this study, a new intrinsic computation technique for GaB called Intrinsic Gallager B (IGaB) is introduced to improve error correction performance. Our simulation results show that the IGaB algorithm provides better error correction performance compared with GaB. GaB and IGaB algorithms are implemented on Field Programmable Gate Array (FPGA) to compare hardware performance.
The Gallager B (GaB), among the hard-decision class of low-density-parity-check (LDPC) algorithms, is an ideal candidate for designing high-throughput decoder hardware. However, GaB suffers from poor error-correction performance. We introduce a probabilistic GaB (PGaB) algorithm that disturbs the decisions made during the decoding iterations randomly with a probability value determined based on experimental studies. We propose a heuristic that switches the decoding from GaB to PGaB after certain number of iterations and show that our heuristic reduces the average iteration count by up to 62% compared with GaB. We evaluate the hardware performance and resource requirement trends of PGaB over three quasicyclic codes using the Xilinx Virtex-6 field programmable gate array. We extend this analysis to performance comparison over our implementations of gradient descent bit flipping (GDBF) and probabilistic GDBF (PGDBF) algorithms for each code studied in this paper. We achieve up to four orders of magnitude better error correction performance than the GaB with less than 1% loss in throughput performance. Our heuristic consistently results with an improvement in maximum operational clock rate across all codes compared with the GDBF and PGDBF.
Low-Density-Parity-Check (LDPC) codes have gained popularity in communication systems and standards due to their capacity-approaching error-correction performance. In this paper, we first expose the tradeoff between decoding performance and hardware performance across three LDPC hard-decision decoding algorithms: Gallager B (GaB), Gradient Descent Bit Flipping (GDBF), and Probabilistic Gradient Descent Bit Flipping (PGDBF). We show that GaB architecture delivers the best throughput while using fewest Field Programmable Gate Array (FPGA) resources, however performs the worst in terms of decoding performance. We then modify the GaB architecture, introduce a new Probabilistic stimulation function (PGaB), and achieve dramatic decoding performance improvement over the GaB, exceeding the performance of GDBF, without sacrificing its superior maximum operating frequency.
This paper presents the performance evaluation of the Probabilistic Gallager B (PGaB), a hard decision message passing Low Density Parity Check (LDPC) Decoder, with respect to the soft decision based decoders MinSum (MS) and Offset-MinSum (OMS). PGaB algorithm relies on introducing deliberate and controlled randomness to some of the exchanged messages of the GaB decoder such that it is able to escape from local minima associated with dominant trapping sets. We show that PGaB delivers higher decoding throughput than soft decision based decoders MS and OMS while using much fewer amount of Field Programmable Gate Array (FPGA) resources. Our Monte-Carlo simulation results show that the decoding performance of the PGaB on Binary Symmetric Channel (BSC) is far better than the deterministic GaB and very close to MS and OMS performances especially in error floor region.
Low-density parity check (LDPC) codes with their near-Shannon capacity limit error correcting performance and iterative decoding algorithm are being evaluated for digital communications applications. For LDPC codes to be used in real systems, their error floors need to be investigated. In this paper, we evaluate the performance of disjoint difference set (DDS)-based LDPC codes (with column weights 3, 4, 5) and array code-based LDPC codes (with column weights 3, 4, 5) in the additive white Gaussian noise (AWGN) channel using a high-speed field programmable gate array (FPGA) simulation platform. The error floor regions (bit error rates down to 10/sup -12/) of those codes are presented. For better performance of array codes, a girth optimization method is proposed and the FPGA evaluation results are presented.
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.
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.