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International Conference on Communications

Lower-Complexity Layered Belief-Propagation Decoding of LDPC Codes

Yeimkuan Chang, Andres I. Vila Casado, Mau-Chung Frank Chang, Richard D. Wesel

Published Jan 1, 2008• 27 citations
Publisher

Abstract

The design of LDPC decoders with low complexity, high throughput, and good performance is a critical task. A well-known strategy is to design structured codes such as quasi- cyclic LDPC (QC-LDPC) that allow partially-parallel decoders. Sequential schedules, such as Layered Belief-Propagation (LBP), converge faster than the traditional flooding schedule while allowing parallel decoding of QC-LDPC codes. In this paper, we propose a novel low-complexity sequential schedule called Zigzag LBP (Z-LBP). Current LBP schedules do not allow partially- parallel architectures in the regime of high-rate codes with small- to-medium blocklengths. Our proposed algorithm can still be implemented in a partially-parallel manner in this regime. Z-LBP provides the same benefits as LBP including faster convergence speed and lower frame error rates than flooding.

DOI
10.1109/icc.2008.225

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The design of LDPC decoders with low complexity, high throughput, and good performance is a critical task. A well-known strategy is to design structured codes such as quasi- cyclic LDPC (QC-LDPC) that allow partially-parallel decoders. Sequential schedules, such as Layered Belief-Propagation (LBP), converge faster than the traditional flooding schedule while allowing parallel decoding of QC-LDPC codes. In this paper, we propose a novel low-complexity sequential schedule called Zigzag LBP (Z-LBP). Current LBP schedules do not allow partially- parallel architectures in the regime of high-rate codes with small- to-medium blocklengths. Our proposed algorithm can still be implemented in a partially-parallel manner in this regime. Z-LBP provides the same benefits as LBP including faster convergence speed and lower frame error rates than flooding.
An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.
In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief propagation (WR-LBP) decoding algorithm, which exploits the residual within a structured layer framework to speed the number of required decoding iterations. The proposed WR-LBP algorithm is assessed against important LDPC decoding algorithms, in terms of the number of iterations required for convergence and the bit error rates.
Layered (or Turbo) decoding of Low-Density Parity-Check (LDPC) codes is considered as a decoding schedule that facilitates partially parallel architectures for performing iterative algorithms based on belief propagation. It has, on one hand, reduced implementation complexity and memory overhead compared to fully parallel architectures and, on the other hand, higher convergence speed compared to both serial and parallel architectures. In this paper, we introduce a general form of shuffling of the parity-check matrix of quasi-cyclic LDPC (QC-LDPC) codes which can split the critical path delay in layered decoding and therefore improve throughput by allowing higher clock rates. We also reveal a valuable property of Latin squares QC-LDPC codes which makes them a good candidate for the proposed shuffling method. As a result of that property, no special caution of choosing offset values in the proposed generalized shuffling method is required.
Abstract Layered decoding (LD) facilitates a partially parallel architecture for performing belief propagation (BP) algorithm for decoding low-density parity-check (LDPC) codes. Such a schedule for LDPC codes has, in general, reduced implementation complexity compared to a fully parallel architecture and higher convergence rate compared to both serial and parallel architectures, regardless of the codeword length or code-rate. In this paper, we introduce a modified shuffling method which shuffles the rows of the parity-check matrix (PCM) of a quasi-cyclic LDPC (QC-LDPC) code, yielding a PCM in which each layer can be produced by the circulation of its above layer one symbol to the right. The proposed shuffling scheme additionally guarantees the columns of a layer of the shuffled PCM to be either zero weight or single weight. This condition has a key role in further decreasing LD complexity. We show that due to these two properties, the number of occupied look-up tables (LUTs) on a field programmable gate array (FPGA) reduces by about 93% and consumed on-chip power by nearly 80%, while the bit error rate (BER) performance is maintained. The only drawback of the shuffling is the degradation of decoding throughput, which is negligible for low values of Eb/N0E_b/N_0Eb​/N0​ Eb/N0 until the BER of 1e−6.
Layered belief-propagation (LBP) with dynamic schedule for low-density parity-check (LDPC) codes using variable nodes residual is presented. The proposed schedule outperforms the conventional LBP with predetermined schedule both in terms of convergence speed and error performance. As compared with node-wised residual belief-propagation (NRBP), it has much lower extra complexity. For LDPC code constructed by PEG, simulation results show that the new schedule offers better error performance and requires much lower extra complexity.
Low-density parity-check (LDPC) codes have been chosen for the fifth-generation (5G) new radio (NR) enhanced Mobile Broad Band (eMBB) data channel. Since NR LDPC codes puncture the first two block columns of the parity-check matrix, the decoding complexity is reduced, but it slows down the convergence rate. In this letter, we propose a fixed schedule that decodes the layers with the least-punctured edges and those with the highest-degree (LPHD), which has much faster convergence speed than conventional schemes. The fixed scheduling schemes cannot take full advantage of the dynamic changes of decoding messages. As a result, the residual-based layered belief propagation (RB-LBP) is proposed to rearrange the layers dynamically among different iterations. Compared with some informed dynamic scheduling (IDS) strategies, RB-LBP reduces the decoding complexity with slight performance loss.