Error exponents for variable-length block codes with feedback and cost constraints


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NAKİBOĞLU B. , Gallager R. G.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.54, no.3, pp.945-963, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 3
  • Publication Date: 2008
  • Doi Number: 10.1109/tit.2007.915913
  • Title of Journal : IEEE TRANSACTIONS ON INFORMATION THEORY
  • Page Numbers: pp.945-963

Abstract

Variable-length block-coding schemes are investigated for discrete memoryless channels with ideal feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error P-e,P-min as a function of constraints R, P, and T on the transmission rate, average cost, and average block length, respectively. For given R and P, the lower and upper bounds to the exponent -(In P-e,P-min)/(T) over bar are asymptotically equal as (T) over bar -> infinity. The resulting reliability function, lim((T) over bar ->infinity) (- In P-e,P-min)/(T) over bar, as a function of R and P, is concave in the pair (R,P) and generalizes the linear reliability function of Burnashev to include cost constraints. The results are generalized to a class of discrete-time memoryless channels with arbitrary alphabets, including additive Gaussian noise channels with amplitude and power constraints.