The Sphere Packing Bound via Augustin's Method

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NAKİBOĞLU B.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.65, no.2, pp.816-840, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1109/tit.2018.2882547
  • Journal Name: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.816-840
  • Keywords: Channel coding, error analysis, error probability, feedback communications, block codes, MEMORYLESS CHANNELS, RENYI DIVERGENCE, CODING THEOREM, OPTIMAL CODES, ERROR, PROBABILITY, REFINEMENT, CONVERSE, RATES
  • Middle East Technical University Affiliated: Yes

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,W- n], assuming that the maximum order 1/2 Renyi capacity among the component channels, i.e. max(t is an element of[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.