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A Modified Serial Decoding Algorithm for Low-Density Parity-Check Codes

Baoyu Tian

Published Jan 1, 2008• 1 citation
OpenAlex

Abstract

A modified serial decoding algorithm for low-density parity-check(LDPC) codes is proposed.Unlike conventional approaches,this algorithm calculates the sum of variable-to-check messages only once at the initialization stage,and then updates it by simple recursions during the decoding stage.Compared with the conventional serial LDPC decoding algorithm,the proposed algorithm has lower computational complexity and higher processing speed without any performance deterioration.

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A modified serial decoding algorithm for low-density parity-check(LDPC) codes is proposed.Unlike conventional approaches,this algorithm calculates the sum of variable-to-check messages only once at the initialization stage,and then updates it by simple recursions during the decoding stage.Compared with the conventional serial LDPC decoding algorithm,the proposed algorithm has lower computational complexity and higher processing speed without any performance deterioration.
Abstract: In this paper, a fast-convergence algorithm is proposed for the decoding of low-density parity-check (LDPC) codes. By putting more weight on the message update from check node to variable node in current iteration, the proposed method speeds up the decoding significantly. Simulation results show that compared with the standard layered min-sum decoding algorithm, the proposed scheme may reduce about 1/6 iteration numbers for LDPC codes used in DVB-S2, with hardware complexity overhead less than 2%. Key–Words: LDPC code, fast convergence decoding algorithm, layered decoding, min-sum algorithm, hardware implementation 1
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
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.
As for the sum-product decoding algorithm of low density parity check(LDPC) codes,a difference-based decoding method is proposed.The main idea is shown as follows: the messages passed on the bipartite graph of LDPC are based on the probability differences,and the updates of both check nodes and message nodes are carried out on some special addition domain.As for the update of check nodes,only some lowest differences can be selected for reducing computational complexity.In contrast with the traditional log-likelyhood-ratio-based(LLR-based) decoding method,the proposed method has much lower complexity,while it has no obvious loss of performance and convergence.
A novel Low-Density Parity-Check(LDPC) decoding algorithm was proposed,which integrates the serial belief propagation mechanism with the normalized BP-Based updating rule.The algorithm propagates the belief according to certain order of the check nodes,thus improves the convergence property of the belief propagation.Meanwhile,the algorithm efficiently lowers the decoding complexity by using the normalized BP-Based updating rule,which makes the algorithm to adapt to the implementation of hardware.Simulation was performed under the AWGN channel and results show that,compared with prior LDPC decoding algorithm,the proposed algorithm is able to accelerate the convergence speed of decoding obviously and enhance the decoding performance significantly.
In this paper, an improved low-complexity sum-product decoding algorithm is presented for low-density parity-check (LDPC) codes. In the proposed algorithm, reduction in computational complexity is achieved by utilizing fast Fourier transform (FFT) with time shift in the check node process. The improvement in the decoding performance is achieved by utilizing an optimized integer constant in the variable node process. Simulation results show that the proposed algorithm achieves an overall coding gain improvement ranging from 0.04 to 0.46 dB. Moreover, when compared with the sum-product algorithm (SPA), the proposed decoding algorithm can achieve a reduction of 42%–67% of the total number of arithmetic operations required for the decoding process.