Non-Asymptotic Converse Bounds Via Auxiliary Channels

This paper presents a new derivation method of converse bounds on the non-asymptotic achievable rate of memoryless discrete channels. It is based on the finite blocklength statistics of the channel, where with the use of an auxiliary channel the converse bound is produced. This methodology is general and initially presented for an arbitrary channel. Afterwards, the main result is specialized for the $q$-ary erasure (QEC), binary symmetric (BSC), and Z channels. Numerical evaluations show improvement in comparison to meta-converse and sphere-packing bounds in the cases of QEC and BSC.