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Video Engineering

Subset-Matrix Based on Short Loop Remove Method for LDLC

Zhu Lianxian

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In order to decode efficiently,a LDLC( Low Density Lattice Codes) check matrix without short loops needs to be constructed. In this paper, a method based on subset-matrix is applied that all 4-loops and 6-loops are removed in subset-matrix,and after combining with Tanner graph,the needed LDLC check matrix can be got. By using subset-matrix,computation complexity has nothing to do with the code length and no new short loop is generated,and the LDLC codes with variable code length can be constructed by using this method. Simulation result in AWGN channel shows that,by applying this method removing all 6-loops,the performance in decoding is much better compared with the LDLC code with no 4-loop.

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The linear block code is called a binary Low Density Parity Check code if its parity-check matrix is a sparse matrix.For the features of parity-check matrix,a LDPC code can be illustrated by a Tanner graph.Cycles,especially short cycles in the Tanner graph,which lead to inefficient decoding and prevent the decoding algorithm from converging to the optimal decoding result.In this paper,we demonstrate that a detection method of short cycle presents generation algorithm of check matrix without cycle 4 and simulates the check-matrix.

Journal of Changshu Institute of Technology•Jan 1, 2011•0 citations
In order to decode efficiently,a LDLC( Low Density Lattice Codes) check matrix without short loops needs to be constructed. In this paper, a method based on subset-matrix is applied that all 4-loops and 6-loops are removed in subset-matrix,and after combining with Tanner graph,the needed LDLC check matrix can be got. By using subset-matrix,computation complexity has nothing to do with the code length and no new short loop is generated,and the LDLC codes with variable code length can be constructed by using this method. Simulation result in AWGN channel shows that,by applying this method removing all 6-loops,the performance in decoding is much better compared with the LDLC code with no 4-loop.
Low density lattice codes (LDLCs) have been shown to approach the AWGN channel capacity and can be decoded by a message passing decoder. The messages passed between check nodes and variable nodes are probability density functions, which are approximated by Gaussian mixtures in existing LDLC decoders. However, in the best-known M-Gaussian decoder, the Gaussian mixtures for approximating variable node messages still contain unnecessary Gaussian components, resulting in exponential decoding complexity in the LDLC degree d. In this paper, an efficient LDLC decoder is proposed from the lattice viewpoint, which only finds out important Gaussian components for approximating the variable node messages. The decoding complexity for the proposed decoder is linear in d. Numerical results show that the proposed decoder can achieve significant complexity saving without degrading the performance compared with the M-Gaussian decoder. In particular, the runtime saving is 75.3% when the code length is 10000 and d is 7.
Low-density Parity check codes (LDPC) are gaining interest for high data rate application in both terrestrial and spatial communications which requires low bit error rate. This paper proposes an algorithm through which the best parity check matrix is obtained for irregular low density parity check codes, which reduces the Bit Error Rate ,Frame Error Rate and computational complexity. Tanner graph also called a bipartite graph format in an Low Density Parity Check (LDPC) code design contains many short cycles; it will produce a computational complexity in a code design process and it degrades the code performance. To overcome this effect, we proposed an new algorithm which obtains a best final parity check matrix. Throughout the paper we will give the detailed description of an efficient algorithm proposed. The complexity is studied graphically and analytically. Using proposed algorithm, cycles of length four observed in corresponding matrix are removed. Each matrix is evaluated over a noisy Additive White Gaussian Noise (AWGN) channel. Bit Error rate and Frame error rate is calculated. The results are compared with randomly generated best parity check matrix. Simulation results shows that proposed method successfully overcomes the computational complexity and meets the near Shannon limit.
Low-density lattice codes (LDLC) are a new type of lattice codes that can be decoded effectively and achieve performance levels near the capacity of the additive white Gaussian noise (AWGN) channel. Earlier designs of LDLC, such as those utilizing Latin squares, relied on high-complexity computer searches to eliminate short cycles. The proposed code construction offers a systematic representation and inherently avoids these issues. This study presents a design for LDLC that is based on Golomb rulers. This approach is deterministic and results in a parity-check matrix that is free of short cycles. In all scenarios examined, the LDLC built on Golomb rulers demonstrated superior frame error rate performance compared to those based on Latin squares. For instance, there is a 1.5 dB improvement observed for a dimension ofn=73\mathrm{n}=73n=73.
The linear block code is called a binary Low Density Parity Check code if its parity-check matrix is a sparse matrix.For the features of parity-check matrix,a LDPC code can be illustrated by a Tanner graph.Cycles,especially short cycles in the Tanner graph,which lead to inefficient decoding and prevent the decoding algorithm from converging to the optimal decoding result.In this paper,we demonstrate that a detection method of short cycle presents generation algorithm of check matrix without cycle 4 and simulates the check-matrix.