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Efficient Implementation of Linear Programming Decoding

机译：线性规划解码的有效实现

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While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the large size of the relaxed LP problem and the inefficiency of using general-purpose LP solvers. This paper explores ideas for fast LP decoding of low-density parity-check (LDPC) codes. By modifying the previously reported Adaptive LP decoding scheme to allow removal of unnecessary constraints, we first prove that LP decoding can be performed by solving a number of LP problems that each contains at most one linear constraint derived from each of the parity-check constraints. By exploiting this property, we study a sparse interior-point implementation for solving this sequence of linear programs. Since the most complex part of each iteration of the interior-point algorithm is the solution of a (usually ill-conditioned) system of linear equations for finding the step direction, we propose a preconditioning algorithm to facilitate solving such systems iteratively. The proposed preconditioning algorithm is similar to the encoding procedure of LDPC codes, and we demonstrate its effectiveness via both analytical methods and computer simulation results.
机译：尽管线性编程（LP）解码比迭代消息传递（IMP）解码为有限长度性能分析提供了更大的灵活性，但由于宽松LP问题的大尺寸和使用通用LP解算器的效率低下。本文探讨了低密度奇偶校验（LDPC）码的快速LP解码的思想。通过修改先前报告的自适应LP解码方案以允许删除不必要的约束，我们首先证明可以通过解决许多LP问题来执行LP解码，其中每个问题最多包含一个来自每个奇偶校验约束的线性约束。通过利用此属性，我们研究了一种稀疏的内点实现，用于解决此线性程序序列。由于内点算法每次迭代中最复杂的部分是线性方程组（通常为病态）系统的求解结果，用于寻找步进方向，因此，我们提出了一种预处理算法，以利于迭代求解此类系统。提出的预处理算法与LDPC码的编码过程相似，我们通过分析方法和计算机仿真结果证明了其有效性。

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