On noise stability of a system with error-correcting codes
V. Siforov · IEEE Transactions on Information Theory · 1956
The problem posed in this paper is to give a relation connecting the noise stability of a communication system in which error-correcting codes are used to the parameters of these codes. The amountxof code combinations is found, which differ from each other by not less than a given number of elements for a given arrangement of all the possible combinations. It is proved that the quantityxdepends on the arrangement of the primary combinations. Inequalities are obtained for the greatest amount of combinationsx_m, for which any two differ by not less thandelements for small and large valuesnof the common number of elements in each code combination. It is established that the probability of distortion,p_n, of a code group in a system with correcting codes satisfies the inequalityp_n < f(p, n, d), wherepis the probability of distortion of one element. The shape of thef(p, n, d)function is found for large values ofn. Graphs of this function are constructed.