Asymptotic Estimates of the Probability of Error for Transmission of Messages over a Discrete Memoryless Communication Channel with a Symmetric Transition Probability Matrix
R. L. Dobrushin · Theory of Probability and Its Applications · 1962
A memoryless channel with a matrix of transaction probabilities $P = \{ P_{ij} \} $ is considered such that any row of the matrix P is a permutation of any other row and any column is a permutation of any other column. It is supposed that $2^{nH} $ possible messages are to be transmitted with the help of words consisting of n symbols. The asymptotic behavior of the error probability for the optimal code is investigated as is the asymptotic behavior of the expectation of the error probability of the randomly chosen code.