冗余随机矩阵集成的平均停集权分布
Average Stopping Set Weight Distribution of Redundant Random Matrix Ensembles
摘要：
定义了冗余随机矩阵系综（简称冗余随机系综），分析了其停止集（SS）的权分布。冗余随机系综由一组具有线性相关行的二进制矩阵组成。这些线性相关的行（冗余行）显着减少了小尺寸的停止集的数量。冗余随机系综的平均SS重量分布的上限和下限。从这些界限，冗余行的数量（对应于BEC上的BP的解码复杂度）和SS权重分布的渐近增长率的临界指数（对应于解码性能）之间的权衡可以导出。它表明，在某些情况下，一个稠密矩阵与线性相关的行产生渐近（即，在小擦除概率的情况下）比具有可比参数的常规LDPC矩阵性能更好。
英文摘要：
In this paper, redundant random matrix ensembles (abbreviated as redundant random ensembles) are defined and their stopping set (SS) weight distributions are analyzed. A redundant random ensemble consists of a set of binary matrices with linearly dependent rows. These linearly dependent rows (redundant rows) significantly reduce the number of stopping sets of small size. An upper and lower bound on the average SS weight distribution of the redundant random ensembles are shown. From these bounds, the trade-off between the number of redundant rows (corresponding to decoding complexity of BP on BEC) and the critical exponent of the asymptotic growth rate of SS weight distribution (corresponding to decoding performance) can be derived. It is shown that, in some cases, a dense matrix with linearly dependent rows yields asymptotically (i.e., in the regime of small erasure probability) better performance than regular LDPC matrices with comparable parameters.
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