无序情况下低密度奇偶校验循环码码字的有效分布
Effective distribution of codewords for Low Density Parity Check Cycle codes in the presence of disorder
摘要：
我们回顾了基于二部图的奇偶校验码所允许的码字的zeta函数表示，然后研究了无序对码字有效分布的影响。随机性（或无序）通过从随机图的集合中对图进行采样并计算集合的平均zeta函数来实现。在图的顶点集的任意大尺寸的限制下，我们发现对应于图圈的非平凡码字的似然性呈指数衰减。该结果提供了网络安全应用中随机化影响的定量估计。
英文摘要：
We review the zeta-function representation of codewords allowed by a parity-check code based on a bipartite graph, and then investigate the effect of disorder on the effective distribution of codewords. The randomness (or disorder) is implemented by sampling the graph from an ensemble of random graphs, and computing the average zeta function of the ensemble. In the limit of arbitrarily large size for the vertex set of the graph, we find an exponential decay of the likelihood for nontrivial codewords corresponding to graph cycles. This result provides a quantitative estimate of the effect of randomization in cybersecurity applications.
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