Geodesic
Asymptotic Estimates of the Probability of Error for Transmission of Messages over
Teoriâ veroâtnostej i ee primeneniâ, Tome 7 (1962) no. 3, pp. 283-311 
R. L. Dobrušin. Asymptotic Estimates of the Probability of Error for Transmission of Messages over. Teoriâ veroâtnostej i ee primeneniâ, Tome 7 (1962) no. 3, pp. 283-311. http://geodesic.mathdoc.fr/item/TVP_1962_7_3_a2/
@article{TVP_1962_7_3_a2,
     author = {R. L. Dobru\v{s}in},
     title = {Asymptotic {Estimates} of the {Probability} of {Error} for {Transmission} of {Messages} over},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {283--311},
     year = {1962},
     volume = {7},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1962_7_3_a2/}
}
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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.