Closed-Form Word Error Rate Analysis for Successive Interference Cancellation Decoders
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We consider the estimation of an integer vector ∈Z^n from the linear observation =+, where ∈R^m× n is a random matrix with independent and identically distributed (i.i.d.) standard Gaussian N(0,1) entries, and ∈̌R^m is a noise vector with i.i.d. N(0,σ^2 ) entries with given σ. In digital communications, is typically uniformly distributed over an n-dimensional box 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) ∈Z^n is fixed and (2) is uniformly distributed over B. We also investigate some properties of the derived WER expressions. Simulated word error probabilities of these two cases agree closely with our theoretical expressions.
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