Non-Asymptotic Converse Bounds Via Auxiliary Channels

Abstract: This paper presents a new derivation method of converse bounds on the non-asymptotic achievable rate of discrete weakly symmetric memoryless 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 method is general and initially is presented for an arbitrary weakly symmetric channel. Afterwards, the main result is specialized for the $q$-ary erasure channel (QEC), binary symmetric channel (BSC), and QEC with stop feedback. Numerical evaluations show identical or comparable bounds to the state-of-the-art in the cases of QEC and BSC, and a tighter bound for the QEC with stop feedback.