Spatially Coupled Sparse Regression Codes: Design and State Evolution Analysis

TL;DR

This paper analyzes the state evolution of spatially coupled sparse regression codes (SC-SPARCs), providing asymptotic predictions of decoding success over Gaussian noise channels and demonstrating how design parameters influence performance.

Contribution

It offers an asymptotic characterization of state evolution equations for SC-SPARCs, enabling prediction of decoding success for any base matrix and rate, and explores parameter effects on decoding.

Findings

State evolution equations accurately predict AMP decoding success.

Decoding succeeds for all rates below channel capacity with the proposed base matrix.

Simulation results validate theoretical predictions.

Abstract

We consider the design and analysis of spatially coupled sparse regression codes (SC-SPARCs), which were recently introduced by Barbier et al. for efficient communication over the additive white Gaussian noise channel. SC-SPARCs can be efficiently decoded using an Approximate Message Passing (AMP) decoder, whose performance in each iteration can be predicted via a set of equations called state evolution. In this paper, we give an asymptotic characterization of the state evolution equations for SC-SPARCs. For any given base matrix (that defines the coupling structure of the SC-SPARC) and rate, this characterization can be used to predict whether or not AMP decoding will succeed in the large system limit. We then consider a simple base matrix defined by two parameters $(\omega, \Lambda)$, and show that AMP decoding succeeds in the large system limit for all rates $R < \mathcal{C}$. The asymptotic result also indicates how the parameters of the base matrix affect the decoding progression. Simulation results are presented to evaluate the performance of SC-SPARCs defined with the proposed base matrix.