Fast Sparse Superposition Codes have Exponentially Small Error Probability for R < C

TL;DR

This paper introduces a fast decoding algorithm for sparse superposition codes on the AWGN channel, demonstrating that reliable communication with exponentially small error probability is achievable at rates below channel capacity.

Contribution

The paper develops an adaptive successive decoding algorithm for sparse superposition codes, enabling efficient decoding with exponentially small error probability for rates below capacity.

Findings

Decoding error probability decreases exponentially with code length.

The proposed algorithm achieves reliable communication at rates R < C.

Sparse superposition codes are effective for AWGN channels with high-dimensional regression techniques.

Abstract

For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. The paper [IEEE Trans. Inform. Theory 55 (2012), 2541 - 2557] investigated decoding using the optimal maximum-likelihood decoding scheme. Here a fast decoding algorithm, called adaptive successive decoder, is developed. For any rate R less than the capacity C communication is shown to be reliable with exponentially small error probability.