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IEEE International Conference on Electronics, Circuits and Systems (ICECS)

Memory efficient implementation of self-corrected min-sum LDPC decoder

Oana Boncalo, Alexandria Amaricai, Valentin Savin

Published Dec 1, 2014• 6 citations
Publisher

Abstract

This paper proposes memory efficient FPGA implementations for layered quasi-cyclic (QC) LDPC decoders, based on the Self-Correcting Min-Sum (SCMS) algorithm. We address the problem of high memory overhead required by layered SCMS based decoders compared to conventional Min-Sum (MS), by proposing two improvements. These require changes in the flow/rule of the conventional SCMS algorithm, in order to avoid storing the signs and the erasure bits of the variable node messages. Three layered LDPC decoders with serial a-posteriori log likelihood ratios (AP-LLR) processing have been implemented: (1) conventional SCMS, (2) SCMS with no check node message signs storage, and (3) SCMS with neither check node message signs nor erasure bits storage. FPGA implementation results for WiMAX (1152, 2304) code show that the third architecture has a resource utilization with 17% less with respect to the one implementing conventional SCMS, and with 11% less than the second architecture. Furthermore, it presents a similar cost to conventional MS, while having a 0.5 dB better error correction capability.

DOI
10.1109/icecs.2014.7049980

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This paper proposes memory efficient FPGA implementations for layered quasi-cyclic (QC) LDPC decoders, based on the Self-Correcting Min-Sum (SCMS) algorithm. We address the problem of high memory overhead required by layered SCMS based decoders compared to conventional Min-Sum (MS), by proposing two improvements. These require changes in the flow/rule of the conventional SCMS algorithm, in order to avoid storing the signs and the erasure bits of the variable node messages. Three layered LDPC decoders with serial a-posteriori log likelihood ratios (AP-LLR) processing have been implemented: (1) conventional SCMS, (2) SCMS with no check node message signs storage, and (3) SCMS with neither check node message signs nor erasure bits storage. FPGA implementation results for WiMAX (1152, 2304) code show that the third architecture has a resource utilization with 17% less with respect to the one implementing conventional SCMS, and with 11% less than the second architecture. Furthermore, it presents a similar cost to conventional MS, while having a 0.5 dB better error correction capability.
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.
Low-density parity-check (LDPC) codes have attracted tremendous attention for their excellent error-correction performance and inherent fitness for high-parallelism implementation. With great complexity reduction and friendly for hardware implementation, the min-sum (MS) decoding algorithm for LDPC codes gains widespread applications in practical. In the MS decoding algorithm, finding the first two minima among input variable-to-check messages is the most complex part. To further reduce the complexity of the MS decoding algorithm, an efficient single-minimum (single-min) based layered MS decoding for quasi-cyclic LDPC (QC-LDPC) codes is proposed in this paper. It is found that statistically the difference between the first minimum and second minimum increases as the decoding becomes more convergent. Accordingly, in the proposed single-min scheme, the second minimum is approximately derived based on the first minimum and an index indicating the convergence degree. Besides, some other metrics that are easily obtained are used to refine the second minimum. Simulation results show that the proposed method can significantly improve the error-correction performance and lower the average number of iterations, compared with the state-of-the-art single-min based MS decoding algorithms.
We propose two decoding algorithms for quasi-cyclic LDPC codes (QC-LDPC) and implement the more efficient one in this paper. These algorithms depend on the split row for the layered decoding method applied to the Min-Sum (MS) algorithm. We designate the first algorithm “Split-Row Layered Min-Sum” (SRLMS), and the second algorithm “Split-Row Threshold Layered Min-Sum” (SRTLMS). A threshold message passes from one partition to another in SRTLMS, minimizing the gap from the MS and achieving a binary error rate of 3 × 10−5 with Imax = 4 as the maximum number of iterations, resulting in a decrease of 0.25 dB. The simulation’s findings indicate that the SRTLMS is the most efficient variant decoding algorithm for LDPC codes, thanks to its compromise between performance and complexity. This paper presents the two invented algorithms and a comprehensive study of the co-design and implementation of the SRTLMS algorithm. We executed the implementation on a Xilinx Kintex-7 XC7K160 FPGA, achieving a maximum operating frequency of 101 MHz and a throughput of 606 Mbps.
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.
In this paper, a new and efficient decoding architecture, Single-Scan Layer Decoding (SLD), is realized in FPGA for multi-rate Quasi-Cyclic LDPC (QC-LDPC) codes. The SLD algorithm simplifies the nodes updating process and messages storing process of the offset min-sum algorithm, speeding up the decoding process and reducing nearly a half of resources consumption. Besides, the SLD algorithm, introducing the semi-parallel architecture into decoding architecture, can increase the convergence rate by 2X and decrease the interconnect complexity of hardware implementation. For multi-rate QC-LDPC Codes in 802.11.n, comparing with float-point software implementation, the degradations of the fixed-point SLD algorithm with 10 iterations in FPGA are all less than 0.ldB and the throughput of different code rates are all above 100Mbps.
In the recent literature, turbo decoding message passing (TDMP) or layered decoding has been proposed for the decoding of low-density parity-check (LDPC) codes using a trellis-based BCJR algorithm in check node units (CNU). We present a new architecture for supporting rate compatible array LDPC codes that uses an offset-based min-sum decoding algorithm instead of the BCJR. The proposed architecture utilizes the value-reuse properties of min-sum and block-serial scheduling of computations, along with TDMP. This novel architecture has the following features: removal of memory needed to store the sum of the variable node messages and the channel values, removal of memory needed to store the variable node messages, 40%-72% savings in storage of extrinsic messages depending on rate of the codes, reduction of routers by 50%, and increase of throughput up to 2times. Implementations on our test-bed FPGA achieve decoded throughputs up to 1.36 Gbps and 2.27 Gbps for each iteration for (5,k) and (3,k) array LDPC codes, respectively. ASIC implementation achieve decoded throughputs up to 5.9 Gbps for each iteration for (5,k) array LDPC codes.