Closed-Form Word Error Rate Analysis for Successive Interference Cancellation Decoders

TL;DR

This paper derives exact closed-form expressions for the word error rates of successive interference cancellation decoders in estimating integer vectors from noisy linear observations, applicable to digital communications.

Contribution

It provides the first closed-form WER formulas for SIC decoders for both fixed and uniformly distributed integer vectors, enhancing understanding of their performance.

Findings

Closed-form WER expressions closely match simulations.

Analysis applies to both fixed and uniformly distributed integer vectors.

Results improve understanding of SIC decoder performance in noisy settings.

Abstract

We consider the estimation of an integer vector $\hbx\in \mathbb{Z}^n$ from the linear observation $\y=\A\hbx+\v$, where $\A\in\mathbb{R}^{m\times n}$ is a random matrix with independent and identically distributed (i.i.d.) standard Gaussian $\mathcal{N}(0,1)$ entries, and $\v\in \mathbb{R}^m$ is a noise vector with i.i.d. $\mathcal{N}(0,\sigma^2 )$ entries with given $\sigma$. In digital communications, $\hbx$ is typically uniformly distributed over an $n$-dimensional box $\mathcal{B}$. For this estimation problem, successive interference cancellation (SIC) decoders are popular due to their low complexity, and a detailed analysis of their word error rates (WERs) is highly useful. In this paper, we derive closed-form WER expressions for two cases: (1) $\hbx\in \mathbb{Z}^n$ is fixed and (2) $\hbx$ is uniformly distributed over $\mathcal{B}$. We also investigate some of their properties in detail and show that they agree closely with simulated word error probabilities.