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Best asymptotic value of the error exponent with random coding on discrete memoryless channels

Published online by Cambridge University Press:  14 July 2016

N. S. Kambo  and
Samar Singh
N. S. Kambo
Affiliation:
Indian Institute of Technology, New Delhi
Samar Singh
Affiliation:
Indian Institute of Technology, New Delhi
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Abstract

Generalizing a technique given by Wolfowitz, we calculate a formula for the asymptotic value of the error exponent with random coding on a discrete memoryless channel. We then evaluate this formula analytically for low rates and show that the exact value given by this formula agrees with the random coding exponent of Gallager and Fano. This proves that their exponent, which was only known to be a bound for low rates, gives the exact value and this brings out the inherent limitation of the random coding method.

Keywords

ASYMPTOTIC VALUE OF THE RANDOM CODING EXPONENTRANDOM CODINGDISCRETE MEMORYLESS CHANNELLOWER BOUND TO RELIABILITYCRITICAL RATE
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 327 - 336
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Fano, R. M. (1961) Transmission of Information. M.I.T. Press and Wiley, New York.Google Scholar
[2] Gallager, R. (1965) A simple derivation of the coding theorem and some applications. IEEE Trans. Information Theory 11, 3–18.Google Scholar
[3] Gallager, R. (1968) Information Theory and Reliable Communication. Wiley, New York.Google Scholar
[4] Shannon, C. E., Gallager, R. G. and Berlekamp, E. R. (1967) Lower bounds to error probability for coding on discrete memoryless channels. Information and Control 10, 65–103 and 522–552.Google Scholar
[5] Wolfowitz, J. (1966) Best exponential upper bounds obtainable by random coding. Unpublished.Google Scholar