LDPC码回路的元胞数组求解算法
|
摘要
LDPC码是性能限与香农限仅差0.0045d B的一种差错控制码,译码采用SPA(和积算法),其性能受Ta nne r图中回路长度和回路数目的影响,回路的存在使译码信息重复迭代,性能下降。论文通过计算机仿真,采用Ma tla b元胞数组,将二元校验矩阵转换为截断树矩阵,实现了求解LDPC码回路的算法,既给出回路的长度,又能得出回路的分支路径,并且能够对所有回路作整体性的描述。
LDPC codes are defined by their sparse parity-check matrices and can be described by bipartite graphs called Tanner graphs. Loops in Tanner graph prevent the sum-product algorithm from converging. Further, loops, especially short loops, degrade the performance of LDPC decoder,because they affect the independence of the extrinsic information exchanged in the iterative decoding. This paper, by graph theory, deduces cut-node tree graph of LDPC code, and depicts it with matrix. On the basis of tree matrix algorithm, whole depictions of loops can be figured out, providing of foundation for further research of relations between loops and LDPC codes' performance.
LDPC codes are defined by their sparse parity-check matrices and can be described by bipartite graphs called Tanner graphs. Loops in Tanner graph prevent the sum-product algorithm from converging. Further, loops, especially short loops, degrade the performance of LDPC decoder,because they affect the independence of the extrinsic information exchanged in the iterative decoding. This paper, by graph theory, deduces cut-node tree graph of LDPC code, and depicts it with matrix. On the basis of tree matrix algorithm, whole depictions of loops can be figured out, providing of foundation for further research of relations between loops and LDPC codes' performance.
引文
[1]R.G.Gallager,Low-Density Parity Check Codes,MIT Press,Cambridge,MA,1963.
[2]D.J.C.Mackay,"Good Error-Correcting Codes Based on Very Sparse Matrices",IEEE Trans.Inform.Theory,vol.45,Mar.1999.
[2]D.J.C.Mackay,"Good Error-Correcting Codes Based on Very Sparse Matrices",IEEE Trans.Inform.Theory,vol.45,Mar.1999.