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Analog Integrated Circuits and Signal Processing

Memory trade-offs in layered self-corrected min-sum LDPC decoders

Oana Boncalo, Alexandru Amaricăi, Petru Florin Mihancea, Valentin Savin

Published Nov 4, 2015• 6 citations
Publisher
DOI
10.1007/s10470-015-0639-3

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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.
Min sum algorithm (MSA) is widely used for decoding Low Density Parity Check (LDPC) codes in many modern Digital Video Broadcasting (DVB) as a simplification for Sum Product Algorithm (SPA) which greatly reduce the implementation complexity. This paper presents a design of modified variable scaling min sum LDPC decoding algorithm for DVB-S2/S2X/T2. The proposed design is a combination between the variable Normalized Min Sum Algorithm (NMSA) and the Offset Min Sum Algorithm (OMSA) which provides a trade-off between decoding complexity and error correcting performance. It improves the use of the Min Sum Algorithm (MSA) by 39%. A proposal for how to implement the proposed algorithm using FPGA is also introduced. The structure used is partially parallel layered decoder architecture.
The near-capacity performance and effective decoding algorithms of Low-Density Parity-Check (LDPC) codes have made them a mainstay of contemporary error correction. With an emphasis on iterative techniques like the Belief Propagation (BP) algorithm, the Min-Sum algorithm, and their variations, this paper offers a thorough analysis of decoding algorithms for LDPC codes. We investigate the trade-offs between various algorithmic techniques’ computational complexity, decoding latency, and error correction performance. Particular focus is placed on new methods and hardware-friendly algorithms that are tailored for next-generation communication systems, such 5 G and beyond.