On the Poor-Verdu conjecture for the reliability function of channels with memory

Abstract

In a previous work, Poor and Verdu (1995) established an upper bound to the reliability function of arbitrary single-user discrete-time channels with memory. They also conjectured that their bound is tight for all coding rates. In this work, we demonstrate via a counterexample involving memoryless binary erasure channels that the Poor-Verdu upper bound is, unfortunately, not tight at low rates. We also examine possible improvements to this bound.