Determination of the mean square error in the transmission of information by a binary irredundant code

Abstract

1. The error dispersion for transmission of information by means of a binary irredundant code over a communication channel with independent errors depends weakly on the asymmetry coefficient α of the channel and decreases only by a factor 1−p when α is varied from 1 to ∞. Therefore, for practical calculations in the case of small p and for any α one may use (6) with an error not exceeding p/(1−p). For accurate calculations, depending on the channel characteristic, one should use (6), (16), or (20). 2. The reduced error dispersion for operation in channels having both independent and burst errors depends weakly on the length n of the code word (in the latter case-for erasure of the symbols encompassed by the error). In particular, for a channel with independent errors the error in using the approximate expressions (7), (17), and (21) does not exceed the value 2/(2П + 1. 3. The dispersion of the error in working in a channel with erasure bursts depends weakly on the lengthl of the burst.