Error Exponents for Variable-Length Block Codes With Feedback and Cost Constraints

摘要

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 $P_{e,min }$ as a function of constraints $R, {cal P},$ and $overline tau $ on the transmission rate, average cost, and average block length, respectively. For given $R$ and $ {cal P}$, the lower and upper bounds to the exponent $-(ln P_{e,min })/overline tau $ are asymptotically equal as $overline tau to infty $. The resulting reliability function, $lim _{overline tau to infty } (-ln P_{e,min })/overline tau $, as a function of $R$ and $ {cal P}$, is concave in the pair $(R, {cal P})$ 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.