Optimality and Rate-Compatibility for Erasure-Coded Packet Transmissions when Fading Channel Diversity Increases with Packet Length

TL;DR

This paper investigates the optimal balance between erasure and channel coding in fading channels where diversity increases with packet length, proposing a rateless coding scheme that minimizes failure probability.

Contribution

It introduces a new PD block fading model and formulates an optimization for rate allocation, revealing that near-perfect erasure coding is optimal under certain conditions.

Findings

Optimal erasure code rate approaches one.

Rateless hybrid coding schemes outperform fixed-rate schemes.

Rate-compatibility influences failure probability trajectories.

Abstract

A message composed of packets is transmitted using erasure and channel coding over a fading channel with no feedback. For this scenario, the paper explores the trade-off between the redundancies allocated to the packet-level erasure code and the channel code, along with an objective of a low probability of failure to recover the message. To this end, we consider a fading model that we term proportional-diversity block fading (PD block fading). For a fixed overall code rate and transmit power, we formulate an optimization problem to numerically find the optimal channel-coding rate (and thus the optimal erasure-coding rate) that minimizes the probability of failure for various approximations of the problem. Furthermore, an interpretation of the results from an incremental redundancy point of view shows how rate-compatibility affects the possible trajectories of the failure probability as a function of the overall code rate. Our numerical results suggest that an optimal, rateless, hybrid coding scheme for a single-user wireless system over the PD block-fading channel should have the rate of the erasure code approach one.