The error exponent of variable-length codes over Markov channels with feedback
IEEE Transactions on Information Theory
Variations on a theme by Schalkwijk and Kailath
IEEE Transactions on Information Theory
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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 Pe,min as a function of constraints R, P, and tau on the transmission rate, average cost, and average block length, respectively. For given R and P, the lower and upper bounds to the exponent -( ln Pe,min )/tau are asymptotically equal as tau rarr infin. The resulting reliability function,limtaurarrinfin(-In Pe,min)/tau as a function of R and V, 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.