论文标题
稀疏的叠加代码，具有无内存频道的旋转不变编码矩阵
Sparse superposition codes with rotational invariant coding matrices for memoryless channels
论文作者
论文摘要
我们最近在[1]中显示了某些结构化编码矩阵的优势（例如部分行 - 正交）对于稀疏的叠加代码，与具有i.i.d的纯随机矩阵相比。条目在理论上和实际矢量下的信息近似消息传递解码。在这里，我们将此结果推广到广义矢量近似消息传播的二进制输入通道[2]。我们关注特定的二进制输出通道，以实现具体性，但是我们基于统计物理学的副本对称方法的分析适用于任何内存通道。我们确认[1]中引入的“光谱标准”是一种编码 - 矩阵设计原理，该原理允许代码以“大截面大小”渐近限制为能力实现，扩展到通用的无内存通道。此外，我们还表明，对于编码矩阵的任意频谱，该编码方案的消失误差属性[3]是通用的。
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both information-theoretically and under practical vector approximate message-passing decoding. Here we generalize this result to binary input channels under generalized vector approximate message-passing decoding [2].We focus on specific binary output channels for concreteness but our analysis based on the replica symmetric method from statistical physics applies to any memoryless channel. We confirm that the "spectral criterion" introduced in [1], a coding-matrix design principle which allows the code to be capacity-achieving in the "large section size" asymptotic limit, extends to generic memoryless channels. Moreover, we also show that the vanishing error floor property [3] of this coding scheme is universal for arbitrary spectrum of the coding matrix.
