Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP Decoding
Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP Decoding
复制标题
通过 AMP 解码实现大容量空间耦合稀疏叠加码
DOI：
10.1109/tit.2021.3083733
复制
发表时间：
2021
影响因子：
2.5
通讯作者：
Venkataramanan, Ramji
中科院分区：
文献类型：
--
作者：
Rush, Cynthia;Hsieh, Kuan;Venkataramanan, Ramji
稀疏叠加码，也被称为稀疏回归码（SPARC），是用于以接近信道容量的速率在AWGN信道上进行有效通信的一类码。在标准SPARC中，码字是独立同分布列的稀疏线性组合高斯设计矩阵，而在空间耦合的设计矩阵中，设计矩阵具有逐块结构，其中高斯项的方差可以跨块变化。一个设计良好的空间耦合结构可以显着提高迭代解码算法，如近似消息传递（AMP）的错误性能。在本文中，我们得到了一个非渐近界的错误概率的空间耦合SPARC与AMP解码。将此界应用于一个简单的带对角设计矩阵，我们证明了空间耦合SPARC与AMP解码实现的AWGN信道的容量。该界限还突出了误差概率的衰减如何取决于空间耦合的双折射的每个设计参数。AMP解码的一个吸引人的特征是其渐近均方误差（MSE）可以通过称为状态演化的确定性递归来预测。我们的结果提供了第一个证明，MSE集中在空间耦合设计的状态演化预测。结合状态演化预测，这一结果表明，空间耦合SPARC与建议的带对角设计的容量实现。使用的证明技术，用于建立主要结果，我们还获得了浓度不等式的AMP的MSE应用于压缩感知与空间耦合的设计矩阵。最后，我们提供了数值模拟结果，证明了空间耦合SPARC的有限长度的错误性能。的性能进行了比较与编码调制方案，使用LDPC码从DVB-S2标准。
Sparse superposition codes, also referred to as sparse regression codes (SPARCs), are a class of codes for efficient communication over the AWGN channel at rates approaching the channel capacity. In a standard SPARC, codewords are sparse linear combinations of columns of an i.i.d. Gaussian design matrix, while in a spatially coupled SPARC the design matrix has a block-wise structure, where the variance of the Gaussian entries can be varied across blocks. A well-designed spatial coupling structure can significantly enhance the error performance of iterative decoding algorithms such as Approximate Message Passing (AMP). In this paper, we obtain a non-asymptotic bound on the probability of error of spatially coupled SPARCs with AMP decoding. Applying this bound to a simple band-diagonal design matrix, we prove that spatially coupled SPARCs with AMP decoding achieve the capacity of the AWGN channel. The bound also highlights how the decay of error probability depends on each design parameter of the spatially coupled SPARC. An attractive feature of AMP decoding is that its asymptotic mean squared error (MSE) can be predicted via a deterministic recursion called state evolution. Our result provides the first proof that the MSE concentrates on the state evolution prediction for spatially coupled designs. Combined with the state evolution prediction, this result implies that spatially coupled SPARCs with the proposed band-diagonal design are capacity-achieving. Using the proof technique used to establish the main result, we also obtain a concentration inequality for the MSE of AMP applied to compressed sensing with spatially coupled design matrices. Finally, we provide numerical simulation results that demonstrate the finite length error performance of spatially coupled SPARCs. The performance is compared with coded modulation schemes that use LDPC codes from the DVB-S2 standard.