A simple derivation of the refined sphere packing bound under certain symmetry hypotheses

Nakiboğlu B.

TURKISH JOURNAL OF MATHEMATICS, cilt.44, sa.3, ss.919-948, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3906/mat-1912-106
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.919-948
  • Anahtar Kelimeler: Hypothesis testing, Berry-Esseen theorem, sphere packing bound, Augustin information measures, constant composition codes, Renyi symmetry, Gaussian channels, ERROR, PROBABILITY, CHANNEL, CODES
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is Omega (n(-0.5(1-E'sp)((R)))) for all codes on certain families of channels (including the Gaussian channels and the nonstationary Renyi symmetric channels) and for the constant composition codes on stationary memoryless channels. The resulting nonasymptotic bounds have definite approximation error terms. As a preliminary result that might be of interest on its own, the trade-off between type I and type II error probabilities in the hypothesis testing problem with (possibly non-stationary) independent samples is determined up to some multiplicative constants, assuming that the probabilities of both types of error are decaying exponentially with the number of samples, using the Berry-Esseen theorem.