# Techniques for improving the finite length performance of sparse superposition codes

## TL;DR

This paper explores techniques to enhance the finite length error performance of sparse superposition codes with AMP decoding, including power allocation, parameter tuning, and outer codes, demonstrating improvements over standard LDPC-coded modulation.

## Contribution

It introduces novel methods for finite length optimization of sparse superposition codes, including an iterative power allocation algorithm and the use of partial outer codes.

## Key findings

- Improved finite length error performance with proposed techniques.
- Steep waterfall error curves achieved with outer codes.
- Competitive performance compared to WiMAX LDPC codes.

## Abstract

Sparse superposition codes are a recent class of codes introduced by Barron and Joseph for efficient communication over the AWGN channel. With an appropriate power allocation, these codes have been shown to be asymptotically capacity-achieving with computationally feasible decoding. However, a direct implementation of the capacity-achieving construction does not give good finite length error performance. In this paper, we consider sparse superposition codes with approximate message passing (AMP) decoding, and describe a variety of techniques to improve their finite length performance. These include an iterative algorithm for SPARC power allocation, guidelines for choosing codebook parameters, and estimating a critical decoding parameter online instead of pre-computation. We also show how partial outer codes can be used in conjunction with AMP decoding to obtain a steep waterfall in the error performance curves. We compare the error performance of AMP-decoded sparse superposition codes with coded modulation using LDPC codes from the WiMAX standard.