Finite-connectivity systems as error-correcting codes.
Finite-connectivity systems as error-correcting codes.
复制标题
有限连接系统作为纠错码。
DOI：
10.1103/physreve.60.5352
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Y. Kabashima
中科院分区：
文献类型：
--
作者：
R. Vicente;D. Saad;Y. Kabashima
我们利用Sourlas [Nature (London) 339,693(1989)]提出的映射到Ising自旋系统来研究奇偶校验码的性能；Europhys。快报，25,159(1994)]。我们研究的代码，其中每个奇偶校验包括从原始数字消息中选择的K位的乘积，每个消息位恰好有C次校验。我们使用复制方法证明，当码率K/C有限时，这些码在K—>∞时饱和香农编码界。然后，我们研究了有限温度情况，以评估模拟退火方法在解码中的使用，研究了有限K情况的性能，并扩展了分析以适应不同类型的噪声信道。讨论了统计物理与信念传播解码器之间的联系，分析了译码本身的动力学特性。进一步深入了解改进代码性能的新方法。
We investigate the performance of parity check codes using the mapping onto Ising spin systems proposed by Sourlas [Nature (London) 339, 693 (1989); Europhys. Lett. 25, 159 (1994)]. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K-->infinity when the code rate K/C is finite. We then examine the finite temperature case to assess the use of simulated annealing methods for decoding, study the performance of the finite K case, and extend the analysis to accommodate different types of noisy channels. The connection between statistical physics and belief propagation decoders is discussed and the dynamics of the decoding itself is analyzed. Further insight into new approaches for improving the code performance is given.