Error detection by binary sparse matrices
Tadashi Wadayama · Journal of Physics Conference Series · 2010
Error detection is a crucial process in an information transmission protocol like TCP for attaining reliable communications over unreliable channels. The most important performance measure for an error detection scheme is its undetected error probability, which is the probability corresponding to the event such that an erroneous received word passes the detection test. The paper reviews the author's results on an analysis of the undetected error probability of ensembles of m × n binary matrices. The ensemble of binary sparse matrices called the Bernoulli ensemble whose members are considered as matrices generated from i.i.d. Bernoulli source is mainly discussed here. The error exponent of the average undetected error probability and closed form expressions for the variance of the undetected error probability will be presented.