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

We consider the detection of an integer vector x̂ ∈ ℤ
ⁿ
from the linear observation y = Ax̂ + v, where A ∈ ℝ
^m×n
is a random matrix with independent and identically distributed (i.i.d.) standard Gaussian N (0, 1) entries, and ν ∈ ℝ
^m
is a noise vector with i.i.d. N (0, σ
²
) entries with given σ. In digital communications, x̂ is typically uniformly distributed over an n-dimensional box B. For this detection problem, successive interference cancellation 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) x̂ ∈ℤ
ⁿ
is fixed and (2) x̂ is uniformly distributed over B. We also investigate some of their properties in detail and show that they agree closely with simulated word error probabilities.