Error Exponents for Variable-length block codes with feedback and cost constraints

Variable-length block-coding schemes are investigated for discrete memoryless channels (DMC) with perfect feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error Pepsi,min as a function of transmission rate R, cost constraint P, and expected block length taumacr. For given P and R, the lower and upper bounds to the exponent -(InPepsi,min)/taumacr are asymptotically equal as taumacr rarrinfin. The reliability function, limtau rarrinfin(-ln Pepsi,min)/taumacr, as a function of P and R, is concave in the pair (P, R) and generalizes the linear reliability function of Burnashev (M.V. Burnashev, 1976) to include cost constraints