Sparse regression codes (SPARCs) are a promising coding scheme that can approach the Shannon limit over Additive White Gaussian Noise (AWGN) channels. Previous works have proven the capacity-achieving property of SPARCs with Gaussian design matrices. We generalize these results to right orthogonally invariant ensembles that allow for more structured design matrices. With the Vector Approximate Message Passing (VAMP) decoder, we rigorously demonstrate the exponentially decaying error probability for design matrices that satisfy a certain criterion with the exponentially decaying power allocation. For other spectra, we design a new power allocation scheme to show that the information theoretical threshold is achievable.

翻译：稀疏回归码（SPARCs）是一种有前景的编码方案，能够在加性高斯白噪声（AWGN）信道下逼近香农极限。已有研究证明了采用高斯设计矩阵的SPARCs具有容量逼近特性。本文将这一结论推广至允许更多结构化设计矩阵的右正交不变系综。对于满足特定准则的设计矩阵，结合向量近似消息传递（VAMP）解码器，我们严格证明了指数衰减的错误概率特性。针对其他谱分布，我们设计了一种新的功率分配方案，论证了信息理论阈值是可实现的。