The Sphere Packing Bound for DSPCs with Feedback à la Augustin

Establishing the sphere packing bound for block codes on the discrete stationary product channels with feedback—which are commonly called the discrete memoryless channels with feedback—was considered to be an open problem until recently, notwithstanding the proof sketch provided by Augustin in 1978. A complete proof following Augustin’s proof sketch is presented to demonstrate its adequacy and to draw attention to two novel ideas that it employs. These novel ideas (i.e., the Augustin’s averaging and the use of subblocks) are likely to be applicable in other communication problems for establishing impossibility results.