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We consider the estimation of an integer vector $\hbx\in \mathbb{Z}^n$ fromthe linear observation $\y=\A\hbx+\v$, where $\A\in\mathbb{R}^{m\times n}$ is arandom matrix with independent and identically distributed (i.i.d.) standardGaussian $\mathcal{N}(0,1)$ entries, and $\v\in \mathbb{R}^m$ is a noise vectorwith i.i.d. $\mathcal{N}(0,\sigma^2 )$ entries with given $\sigma$. In digitalcommunications, $\hbx$ is typically uniformly distributed over an$n$-dimensional box $\mathcal{B}$. For this estimation problem, successiveinterference cancellation (SIC) decoders are popular due to their lowcomplexity, and a detailed analysis of their word error rates (WERs) is highlyuseful. 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 showthat they agree closely with simulated word error probabilities.

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