A derivation of the asymptotic random-coding prefactor

This paper studies the subexponential prefactor to the random-coding bound for a given rate. Using a refinement of Gallager's bounding techniques, an alternative proof of a recent result by Altuğ and Wagner is given, and the result is extended to the setting of mismatched decoding.

[1]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[2]  S. Shamai,et al.  Information rates and error exponents of compound channels with application to antipodal signaling in a fading environment , 1993 .

[3]  Imre Csiszár,et al.  Channel capacity for a given decoding metric , 1995, IEEE Trans. Inf. Theory.

[4]  R. L. Dobrushin,et al.  Asymptotic Estimates of the Probability of Error for Transmission of Messages over a Discrete Memoryless Communication Channel with a Symmetric Transition Probability Matrix , 1962 .

[5]  Robert G. Gallager,et al.  The random coding bound is tight for the average code (Corresp.) , 1973, IEEE Trans. Inf. Theory.

[6]  H. Vincent Poor,et al.  Channel coding: non-asymptotic fundamental limits , 2010 .

[7]  Elwyn R. Berlekamp,et al.  Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. II , 1967, Inf. Control..

[8]  R. R. Bahadur,et al.  On Deviations of the Sample Mean , 1960 .

[9]  Albert Guillén i Fàbregas,et al.  Mismatched Decoding: Finite-Length Bounds, Error Exponents and Approximations , 2013, ArXiv.

[10]  Emre Telatar,et al.  Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit , 2000, IEEE Trans. Inf. Theory.

[11]  Imre Csiszár Generalized cutoff rates and Renyi's information measures , 1995, IEEE Trans. Inf. Theory.

[12]  Albert Guillén i Fàbregas,et al.  Ensemble-tight error exponents for mismatched decoders , 2012, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[13]  Aaron B. Wagner,et al.  Refinement of the Random Coding Bound , 2012, IEEE Transactions on Information Theory.

[14]  N. Sloane,et al.  Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. I , 1993 .

[15]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[16]  Shlomo Shamai,et al.  On information rates for mismatched decoders , 1994, IEEE Trans. Inf. Theory.

[17]  G. A. Barnard,et al.  Transmission of Information: A Statistical Theory of Communications. , 1961 .

[18]  Li Peng,et al.  Expurgated Random-Coding Ensembles: Exponents, Refinements, and Connections , 2013, IEEE Transactions on Information Theory.

[19]  H. Vincent Poor,et al.  Channel Coding Rate in the Finite Blocklength Regime , 2010, IEEE Transactions on Information Theory.

[20]  Aaron B. Wagner,et al.  Refinement of the sphere-packing bound , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[21]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.