Capacity-achieving sparse superposition codes with spatially coupled VAMP decoder

2025-04-18

AI Summary

To address the challenge of enabling Sparse Regression Codes (SPARCs) to approach Shannon capacity over Gaussian channels, this paper proposes a spatially coupled Vector Approximate Message Passing (SC-VAMP) decoder along with a tailored spatially coupled design matrix. The key contribution is the first integration of spatial coupling into the VAMP decoding framework for SPARCs, thereby overcoming structural constraints imposed by conventional exponential power allocation schemes. Through rigorous state evolution (SE) analysis, we prove that the proposed SC-VAMP achieves Shannon capacity on Gaussian channels. Experimental results demonstrate that, at comparable computational complexity, SC-VAMP significantly reduces section error rates compared to standard VAMP decoders employing exponential power decay. The implementation code is publicly available.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Sparse superposition (SS) codes provide an efficient communication scheme over the Gaussian channel, utilizing the vector approximate message passing (VAMP) decoder for rotational invariant design matrices. Previous work has established that the VAMP decoder for SS achieves Shannon capacity when the design matrix satisfies a specific spectral criterion and exponential decay power allocation is used. In this work, we propose a spatially coupled VAMP (SC-VAMP) decoder for SS with spatially coupled design matrices. Based on state evolution (SE) analysis, we demonstrate that the SC-VAMP decoder is capacity-achieving when the design matrices satisfy the spectra criterion. Empirically, we show that the SC-VAMP decoder outperforms the VAMP decoder with exponential decay power allocation, achieving a lower section error rate. All codes are available on https://github.com/yztfu/SC-VAMP-for-Superposition-Code.git.

Problem

• Enhancing sparse superposition codes with SC-VAMP decoder
• Achieving Shannon capacity via spatially coupled design matrices
• Improving error rates compared to traditional VAMP decoders

Innovation

• Spatially coupled VAMP decoder for SS codes
• Capacity-achieving with spectral criterion matrices
• Lower error rate than exponential decay allocation