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IEEE Vehicular Technology Conference

Low Complexity LDPC Decoding Techniques with Adaptive Selection of Edges

Kwangho Shin, Jungwoo Lee

Published Apr 1, 2007• 2 citations
Publisher

Abstract

In this paper, we propose low complexity LDPC decoding algorithms with variable number of edges. The main idea of this paper is to use the bit nodes selectively instead of using all the connected bit nodes. The proposed algorithms choose the bit node selectively when calculating the check node update equation. First, we study the relationship between the number of bit nodes for updating check node and the performance of the BP decoding algorithm. Two selective algorithms are proposed accordingly. The first algorithm (algorithm 1) does not use the bit nodes whose values are highly reliable when calculating the check node update equation. In the second algorithm (algorithm 2), we increase the number of bit nodes to update check node each time we have a decoding failure. These two algorithms have lower complexity with small performance degradation compared to the LLR-BP based decoding algorithm. These algorithms reduce the computational complexity at high SNR more than they do at low SNR.

DOI
10.1109/vetecs.2007.455

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In this paper, we propose low complexity LDPC decoding algorithms with variable number of edges. The main idea of this paper is to use the bit nodes selectively instead of using all the connected bit nodes. The proposed algorithms choose the bit node selectively when calculating the check node update equation. First, we study the relationship between the number of bit nodes for updating check node and the performance of the BP decoding algorithm. Two selective algorithms are proposed accordingly. The first algorithm (algorithm 1) does not use the bit nodes whose values are highly reliable when calculating the check node update equation. In the second algorithm (algorithm 2), we increase the number of bit nodes to update check node each time we have a decoding failure. These two algorithms have lower complexity with small performance degradation compared to the LLR-BP based decoding algorithm. These algorithms reduce the computational complexity at high SNR more than they do at low SNR.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
At present, Low-Density Parity-Check (LDPC) codes widely used in many fields of communications have the best performance of all the Error Correcting Codes (ECC). This paper mainly studies the decoding algorithms of LDPC. It proposes an improved algorithm which is named Check-Variable nodes Hybrid(CVH) algorithm on the basis of the existing algorithms. The CVH algorithm can reduce the computational complexity during the check-node update while overcome with the correlation between the variable-node news in a code with circles. As well as, comparing with the original algorithms the performance of the new one saves 0.1 and 0.3 dB than Log-likelihood Ratios (LLR) Belief Propagation (BP) and BP - based algorithms under Additive White Gaussian Noise (AWGN) channel when the Bit Error Rate (BER) falls to through the simulation. This point shows that this algorithm can increase the decoding performance and reduce the error rate effectively.
In this paper, we introduce a computationally efficient selective node update algorithm for the decoding of low-density parity check codes. Unlike the standard sum-product algorithm, where all bit and check nodes are updated at each decoding iteration, the developed algorithm only updates unreliable check and bit nodes. A simple reliability criteria is developed to determine the active bit and check nodes per decoding iteration. Based on the developed technique, significant computation reductions are achieved with very little or no loss in the BER performance of the LDPC codes. At a WER of 10-5, 91.8% and 72.7% check node and 80% and 41% bit node computation reductions are obtained for a (96, 48) and a (504, 252) LDPC code, respectively. The proposed method can be implemented with a slight modification to the standard sum-product decoding algorithm with negligible additional hardware complexity. From a hardware point of view, the proposed algorithm offers power reductions proportional to the computation savings and it leads to higher decoding speeds in serial implementations by decreasing the number of required memory accesses
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.
Non-binary LDPC codes are promising error correcting techniques with very good performance, especially for high order fields. Using higher order fields enhances performance but, at the same time, increases decoding complexity. Several methods have been proposed to reduce this complexity, such as sub-optimal decoding algorithms or techniques aiming at reducing the number of iterations. In this paper, a technique for selective check nodes update is presented enabling a complexity reduction at the level of iteration in the non-binary case. More than 35% of complex updates can be saved in a large SNR region, with parameters that can be tuned according to the desired complexity/performance ratio.