Rateless Coding for Gaussian Channels

TL;DR

This paper introduces a new construction of rateless codes for Gaussian channels that are capacity-achieving, low in complexity, and adaptable to time-varying conditions, using layered encoding and successive decoding techniques.

Contribution

The paper presents the first known construction of perfect rateless codes with low-complexity decoding for Gaussian channels, including practical three-rate codes and near-perfect variants.

Findings

Existence of perfect rateless codes with low complexity

Design of a practical three-rate code family

Development of near-perfect codes requiring fewer layers

Abstract

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.