Arimoto Channel Coding Converse and Rényi Divergence
نویسندگان
چکیده
Arimoto [1] proved a non-asymptotic upper bound on the probability of successful decoding achievable by any code on a given discrete memoryless channel. In this paper we present a simple derivation of the Arimoto converse based on the dataprocessing inequality for Rényi divergence. The method has two benefits. First, it generalizes to codes with feedback and gives the simplest proof of the strong converse for the DMC with feedback. Second, it demonstrates that the sphere-packing bound is strictly tighter than Arimoto converse for all channels, blocklengths and rates, since in fact we derive the latter from the former. Finally, we prove similar results for other (non-Rényi) divergence measures.
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Strong converse to the quantum channel coding theorem
A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown. The results and their derivations are mostly straightforward extensions of the classical counterparts which were established by Arimoto, except that more careful treatment is necessary here due to the nonc...
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[I] D. Slepian and J. K. Wolf, “A coding theorem for multiple access channel with correlated sources,” BeN. Sys?. Tech. J, vol. 52, pp. 10371076, 1973. [2] T. M. Cover, “Broadcast channels,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 2-14, 1972. [3] E. C. van der Meulen, “Random coding theorem for the general discrete memoryless broadcast channel,” IEEE Trans. Inform. Theory, vol. IT-21, pp. 1...
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