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Two Phases GC-LDPC Decoding Aided with Early Termination and Forced Convergece

Kun Zhu, Hongwen Yang

Published Jul 2, 2024• 0 citations
Publisher

Abstract

The fast decoding of low-density parity-check (LDPC) is crucial for its future applications. In this paper, we propose to use Early Termination (ET) and Force Convergence (FC) techniques to accelerate the decoding of two new local/global two-phases decoding algorithms to reduce the Globally Coupled (GC) LDPC codes. Specifically, ET is applied in the local decoding phase of two- phases decoding of GC-LDPC codes to skip the local decoding which is highly likely to fail and avoid the unnecessary iterations. FC is applied in global decoding phase where converged variable nodes are identified and removed from Tanner graph and the decoding can be speed up shrinking parity check matrices. Two variants are proposed for the ET operation in local decoding phase. ET-1 merely stops iteration if it meets the stopping criterion while in ET-1, the iteration number saved in local decoding is added up in global decoding to improve the decoding performance. The simulation results show that the ET-1-FC scheme can save up to 42% decoding time complexity in the low SNR region while keeping the error rate performance nearly unchanged, the ET-2-FC can improve the error rate performance by 0.18dB at bit error rate 0.001 or 0.23dB at frame error rate 0.1. In the waterfalling region of BER/FER curves, both schemes can save about 25% decoding time complexity.

DOI
10.20944/preprints202407.0158.v1

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The fast decoding of low-density parity-check (LDPC) is crucial for its future applications. In this paper, we propose to use Early Termination (ET) and Force Convergence (FC) techniques to accelerate the decoding of two new local/global two-phases decoding algorithms to reduce the Globally Coupled (GC) LDPC codes. Specifically, ET is applied in the local decoding phase of two- phases decoding of GC-LDPC codes to skip the local decoding which is highly likely to fail and avoid the unnecessary iterations. FC is applied in global decoding phase where converged variable nodes are identified and removed from Tanner graph and the decoding can be speed up shrinking parity check matrices. Two variants are proposed for the ET operation in local decoding phase. ET-1 merely stops iteration if it meets the stopping criterion while in ET-1, the iteration number saved in local decoding is added up in global decoding to improve the decoding performance. The simulation results show that the ET-1-FC scheme can save up to 42% decoding time complexity in the low SNR region while keeping the error rate performance nearly unchanged, the ET-2-FC can improve the error rate performance by 0.18dB at bit error rate 0.001 or 0.23dB at frame error rate 0.1. In the waterfalling region of BER/FER curves, both schemes can save about 25% decoding time complexity.
To enhance the decoding efficiency of Globally Coupled (GC) LDPC codes, we incorporated Early Termination (ET) and Forced Convergence (FC) into the local/global two-phase decoding algorithm to expedite the decoding process. The two-phase decoding scheme integrates the ET technique to halt unnecessary iterations in the local decoding phase while employing the FC technique to accelerate convergence in the global phase decoding. The application of ET technology in the local decoding of GC-LDPC codes will not cause performance loss as in traditional block codes and will cause considerable complexity gains. For a longer code length and larger convergence differences between nodes' global codes, the FC technique operates more efficiently in global code than local code. Two variants are proposed for the ET scheme in the local decoding, namely ET-1 and ET-2. The initial variant, ET-1, predicts whether local decoding can be successful according to data characteristics and stop the local decoding iteration that is not expected to be successful in time. In the case of ET-2, the saved local iterations are transformed to global decoding equally. The results show that ET-1 saves considerable decoding time complexity and ET-2 improves the performance of the GC-LDPC code with the same decoding time complexity. The combined approach of ET-1 with FC reduces the decoding time complexity up to 42% at a low Signal Noise Rate region while maintaining its performance; ET-2-FC two-phase decoding saves approximately 25% decoding time complexity while improving the BER by about 0.18 dB and FER by about 0.23 dB.
In this paper, we present a new forced convergence decoding scheme for LDPC codes. We remove the early detected variable nodes from the Tanner graph and thus the parity matrix shrinks iteration by iteration and the decoding complexity can be reduced. When the parity check matrix shrinks to zero before the maximum iteration, we get a chance to detect the wrong deletion and, for the decodable codewords, most of such failure can be recovered by restoring the original Tanner graph and resuming the decoding in the remaining iterations. Simulations results indicate that the proposed method can reduce the decoding complexity significantly while keep the error rate performance unchanged or even better.
An efficient early stopping criterion based on the evolution of the number of reliable variable nodes (NRVN) is proposed for low density parity check (LDPC) codes in this paper. This criterion can significantly reduce the average number of iterations (ANI) at low to middle signal to noise ratios (SNRs) with minimal performance degradation. Furthermore, a hybrid decoding method is presented to reduce the decoding complexity of LDPC codes by combining the proposed stopping criterion and forced convergence (FC) decoding algorithm. Compared with the classic belief propagation (BP) decoding, significant computation complexity reduction can be achieved with small computation overhead.
A two-stage decoding algorithm to lower the error-floor for low-density parity-check (LDPC) codes is presented. An efficient stopping criterion is proposed to avoid unnecessary iterations in the first stage. If the stopping criterion is reached, the first stage decoding will be terminated and the second stage decoding will be started, where the unsuccessfully decoded words are re-decoded by manipulating the log-likelihood ratio (LLR) of two types of specifically selected variable nodes. Simulation results show that the proposed algorithm can effectively lower the error floor of LDPC codes while maintaining a low decoding complexity.
Energy consumption is a major issue for LDPC decoding. To save LDPC iterative process energy, early terminations are commonly used. Traditional parity check equation is used but has a growing complexity as the block size increases. This requires a large overhead in term of area. This paper proposes an ultra-low complexity early termination (ET) scheme with a small loss of bit error rate performance based on the layer stopping (LS) criterion. The proposed ET scheme is performed by checking the number of convergent layers stopped by the LS criterion with a preset threshold. Compared with other ET schemes, the proposed ET scheme has a negligible hardware overhead and an acceptable bit error rate performance.
Low-density parity-check (LDPC) codes are one of the most popular linear block codes have ever been used in the communication system.The standard two-phase message passing decoding (TPMPD) algorithm and the layered message-passing decoding (LMPD) algorithm are widely used in LDPC decoder.However, the convergence speed of LMPD algorithm is much faster than that of TPMPD algorithm, particularly in the condition of high signal noise ratio (SNR).In this paper, we propose an early termination criterion for quasi-cyclic low-density parity-check (QC-LDPC) codes based on LMPD algorithm with fast convergence speed.The strategy is to dynamically reprocesses the uncorrected related layers while skipping the corrected ones.Simulations show that 3% reduction in terms of iteration numbers can be achieved with no performance loss compared to the traditional termination strategies, such as hard decision aided (HDA) strategy and parity check equations (PCE) strategy.Furthermore, the optimized early termination strategy achieves low complexity in hardware implementation.