论文标题
用通用旋转不变编码矩阵下的鞋面解码下的稀疏叠加代码
Sparse superposition codes under VAMP decoding with generic rotational invariant coding matrices
论文作者
论文摘要
稀疏叠加代码最初是在高斯通道上作为能力实践传播方案的建议，其编码矩阵是由I.I.D制成的。高斯条目。我们将此编码方案扩展到具有任意频谱的旋转不变矩阵的更通用的集合，其中包括高斯集团作为特殊情况。我们进一步介绍和分析了基于矢量近似消息通话（VAMP）的解码器。基于标准复制品对称潜在理论和状态进化分析，我们的主要发现是与I.I.D相比的某些结构化矩阵（例如部分行 - 正交）的某些结构化合物的优势。矩阵，以及vamp阈值的频谱独立的上限。最重要的是，我们得出了一个简单的“光谱标准”，使该方案在同一时间进行容量方面的方案，同时具有最佳的算法阈值，在“大截面大小”渐近极限中。因此，我们的结果为这种有希望的沟通计划中的编码矩阵提供了实用的设计原理。
Sparse superposition codes were originally proposed as a capacity-achieving communication scheme over the gaussian channel, whose coding matrices were made of i.i.d. gaussian entries.We extend this coding scheme to more generic ensembles of rotational invariant coding matrices with arbitrary spectrum, which include the gaussian ensemble as a special case. We further introduce and analyse a decoder based on vector approximate message-passing (VAMP).Our main findings, based on both a standard replica symmetric potential theory and state evolution analysis, are the superiority of certain structured ensembles of coding matrices (such as partial row-orthogonal) when compared to i.i.d. matrices, as well as a spectrum-independent upper bound on VAMP's threshold. Most importantly, we derive a simple "spectral criterion " for the scheme to be at the same time capacity-achieving while having the best possible algorithmic threshold, in the "large section size" asymptotic limit. Our results therefore provide practical design principles for the coding matrices in this promising communication scheme.
