On Undetected Error Probability of Binary Matrix Ensembles

Abstract— In this paper, analysis on undetected error probability of ensembles of m × n binary matricies is presented. Two ensembles are considered: One is an ensemble of dense matrices and another is an ensemble of sparse matrices. The main contributions of this work are (i) derivation of the error exponent of average undetected error probability and (ii) closed form expressions of the variance of undetected error probability. It is shown that the behavior of the exponent for a sparse ensemble is fairly different from that for a dense ensemble. The analysis for the sparse ensemble indicates the error detection performance achievable with time complexity O(n). The variance of undetected error probability leads to a concentration result. Furthermore, as a byproduct of the proof of the variance formulas, simple covariance formulas of the weight distribution have been derived.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Tadashi Wadayama
• Keywords: Average Undetected Error, CORR 2007, Education, Sparse Ensemble, Undetected Error Probability