The Sphere Packing Bound for Memoryless Channels

Nakiboglu B.

PROBLEMS OF INFORMATION TRANSMISSION, cilt.56, sa.3, ss.201-244, 2020 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1134/s0032946020030011
  • Dergi Adı: PROBLEMS OF INFORMATION TRANSMISSION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Sayfa Sayıları: ss.201-244
  • Anahtar Kelimeler: Augustin's method, sphere packing exponent, error exponent, reliability function, memoryless channels, Gaussian channels, Poisson channels, SIMPLE DERIVATION, ERROR, PROBABILITY, CAPACITY, REFINEMENT
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Sphere packing bounds (SPBs)-with prefactors that are polynomial in the block length-are derived for codes on two families of memoryless channels using Augustin's method: (possibly nonstationary) memoryless channels with (possibly multiple) additive cost constraints and stationary memoryless channels with convex constraints on the composition (i.e., empirical distribution, type) of the input codewords. A variant of Gallager's bound is derived in order to show that these sphere packing bounds are tight in terms of the exponential decay rate of the error probability with the block length under mild hypotheses.