The Sphere Packing Bound via Augustin's Method

Abstract

A sphere packing bound (SPB) with a prefactor that is polynomial in the block length $n$ is established for codes on a length $n$ product channel $W_{[1,n]}$ assuming that the maximum order $1/2$ Renyi capacity among the component channels, i.e. ${\max }_{t\in [1,n]}{C}_{1/2,W_t}$, is $O(\ln n)$. The reliability function of the discrete stationary product channels with feedback is bounded from above by the sphere packing exponent. Both results are proved by first establishing a non-asymptotic SPB. The latter result continues to hold under a milder stationarity hypothesis.

30 pages. An error in the statement of Lemma 2 is corrected. The change is inconsequential for the rest of the paper

References in corpus (1)

• The Augustin Center and The Sphere Packing Bound For Memoryless Channels

Cited by in corpus (6)

• Quantum Sphere-Packing Bounds with Polynomial Prefactors
• The Augustin Capacity and Center
• Properties of Noncommutative Renyi and Augustin Information
• The Sphere Packing Bound For Memoryless Channels
• Refined Strong Converse for the Constant Composition Codes
• The Sphere Packing Bound for DSPCs with Feedback a la Augustin