论文标题
稀疏的平价检查矩阵
Sparsifying Parity-Check Matrices
论文作者
论文摘要
奇偶校验检查矩阵（PCM）用于定义线性误差校正代码，并确保在噪声通道上可靠的信息传输。这种代码的代码集集是此二进制矩阵的空空间。 我们考虑将奇偶校验检查矩阵中一项的数量最小化的问题。在最大样品（ML）解码方法中，PCM中的数量与解码消息所需的时间直接相关。我们提出了一个简单的矩阵行操作启发式，可以改变PCM，但不能改变代码本身。我们应用模拟的退火和贪婪的本地搜索，以获取具有少数一个条目的PCM，即使用主流硬件时几分钟或几个小时内。所得矩阵提供更快的ML解码程序，尤其是对于大型代码。
Parity check matrices (PCMs) are used to define linear error correcting codes and ensure reliable information transmission over noisy channels. The set of codewords of such a code is the null space of this binary matrix. We consider the problem of minimizing the number of one-entries in parity-check matrices. In the maximum-likelihood (ML) decoding method, the number of ones in PCMs is directly related to the time required to decode messages. We propose a simple matrix row manipulation heuristic which alters the PCM, but not the code itself. We apply simulated annealing and greedy local searches to obtain PCMs with a small number of one entries quickly, i.e. in a couple of minutes or hours when using mainstream hardware. The resulting matrices provide faster ML decoding procedures, especially for large codes.
