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Journal of Physics Conference Series

Anti-short girth serial update decoding algorithm of GF(q) LDPC codes

Xin Chen, Bo Li, Yanbin Chen

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Abstract A serial Fast Fourier Transform Belief Propagation (FFT-BP) algorithm with low complexity of non-binary LDPC codes decoding is presented in this paper to reduce the effects of short girth. During iteration, part of the variable nodes with short girths will just send messages to its neighbor, which are in the same short girth and avoid the messages from them. In the next iteration decoding, this part of the nodes updates and the newly updated node with sort girth stops updating. Simulations show that the proposed algorithm achieves a better gain to the standard algorithm and reduces complexity at the same time.

DOI
10.1088/1742-6596/1237/2/022171

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Abstract A serial Fast Fourier Transform Belief Propagation (FFT-BP) algorithm with low complexity of non-binary LDPC codes decoding is presented in this paper to reduce the effects of short girth. During iteration, part of the variable nodes with short girths will just send messages to its neighbor, which are in the same short girth and avoid the messages from them. In the next iteration decoding, this part of the nodes updates and the newly updated node with sort girth stops updating. Simulations show that the proposed algorithm achieves a better gain to the standard algorithm and reduces complexity at the same time.
Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.
A low complexity serial Fast Fourier Transform Belief Propagation (FFT-BP) algorithm for decoding non-binary low-density parity-check (LDPC) codes use unsymmetrical message transmission scheme between bit nodes and check nodes is presented. Before each step of iteration, every symbol node's reliability was evaluated based on high reliable check number and pseudo a posterior probability (APP). The variable nodes with high reliability will just send messages to its neighbour and avoid the messages from them. Compared to the previous traditional message transmission method, it can use the messages adaptively, and therefore provide better decoding quality and computation complexity reduction. Simulations show that the proposed method could improve performance and reduce complexity at the same time compared with the conventional FFT-BP decoding algorithm.
To solve the problem of high computational complexity and inconvenient for hardware implementation in original decoding algorithm for non-binary LDPC codes,two simplified decoding algorithms are introduced for nonbinary LDPC codes: the fast Fourier transform belief propagation(FFT-BP) decoding algorithm and the Log-domain belief propagation(Log-BP) decoding algorithm. The performance comparison between two different decoding algorithms for LDPC Codes over GF(q) is investigated at high code rates(1/2~1) over AWGN channel.The performance curves show that by the decreasing of code rate,both coding gains and the distances from Shannon limit increase with the two algorithms,which means that non-binary LDPC Codes are suit for applications at high rates.Meanwhile it is shown that Log-BP decoding algorithm may contribute a considerable improvement in computational complexity at the cost of sacrificing some performance, which is important for Log-BP decoding algorithm to be applied in hardware implementation.
We propose a new belief propagation (BP) decoding algorithm for fast convergence decoding of regular LDPC codes. The fast convergence is achieved by grouping and scheduling updates of nodes on a bipartite-graph without additional computations or approximations. For this reason, the proposed algorithm can be applied to a serially constructed decoder, and can reduce the power consumption and decoding delay of the decoder. Simulation results show that the convergence speed of the proposed algorithm depends on the degree, d/sub v/, of the variable-nodes of the bipartite-graph, and the average number of iterations of the decoder can be reduced to (d/sub v/-1)/d/sub v/ by using the proposed algorithm without performance degradation or additional computation.
The decoding algorithms of Nonbinary low-density parity-check (NB-LDPC) codes mainly include Belief Propagation (BP), Fast Fourier Transforms (FFT) and Extended Min-Sum (EMS). Among these decoding algorithms, although EMS has the lowest decoding complexity, there is still room for improvement. Therefore, this paper proposes a new algorithm based on the EMS algorithm to further improve the decoding complexity and performance. In order to reduce complexity, an adaptive truncation rule is added to the decoding process. The adaptive truncation rule chooses the length of automatic truncation to reduce the average number of iterations. Thus, the complexity of decoding algorithm is reduced. Besides the weighting factors is added to the variable update iteration process, which effectively improves the decoding performance. The results show that the proposed algorithm has about 0.9 dB gain compared with the EMS decoding algorithm when the bit error rate (BER) is 10--4and the Galois field GF(q) (q16).
Two different decoding algorithms for non-binary LDPC codes: the fast Fourier transform belief propagation (FFT-BP) decoding algorithm and the Log-domain belief propagation (Log-BP) decoding algorithm are introduced in this paper. Their performance advantage of two different decoding algorithms for LDPC Codes over GF(q) is investigated at high code rates (1/2~1) over AWGN channel. The performance curves show that with the decreasing of code rate, both coding gains and the distances from Shannon limit increase under the two algorithms, which means for non- binary LDPC Codes to be suitable for applications at high rates. Meanwhile it is shown that Log-BP decoding algorithm may contribute a considerable saving in computational complexity at the cost of sacrifice small performance, which is important for Log-BP decoding algorithm to be applied in hardware implementation.