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

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2 Author(s)
Nakiboglu, B. ; Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA ; Gallager, R.G.

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.

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Information Theory, IEEE Transactions on  (Volume:54 ,  Issue: 3 )