Weighted Unequal Error Protection over a Rayleigh Fading Channel

TL;DR

This paper compares power-domain superposition and orthogonal resource allocation for unequal error protection over Rayleigh fading channels, showing PDS slightly outperforms ORA with minimal performance gap.

Contribution

It provides asymptotic and finite blocklength analysis, optimal resource allocation algorithms, and performance bounds for two schemes in Rayleigh fading channels.

Findings

PDS outperforms ORA by less than 2% in performance.

The performance gap between asymptotic and finite blocklength is about 10% for n=1000.

Numerical bounds show small performance differences in practical regimes.

Abstract

We study a variant of unequal error protection in channel coding, where the message bit string is divided into a finite number of blocks and the maximization objective is a weighted sum of per-block decoding success probabilities. The channel model is quasi-static Rayleigh fading with channel state information available to the receiver but unavailable to the transmitter. We analyze the asymptotic and finite blocklength performance of two achievability schemes, one based on power-domain superposition (PDS) and another based on orthogonal resource allocation (ORA), also known as time-sharing. Upper bounds on the optimal number of blocks to transmit are derived. Algorithms to compute the optimal power and time splits for the two schemes are given. Simplified algorithms to compute locally optimal power and time splits are also given. Our results show that PDS outperforms ORA, but the performance differential is less than 2% in both the asymptotic and finite blocklength regimes (Figures 4 - 6). For both PDS and ORA, numerical results also upper bound the gap between the asymptotic and finite blocklength performance by approximately 10% for n = 1000 and 3% for n = 5000 (Figures 7 - 10).