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- W2033757125 abstract "Gallager [1] and Gallager, Shannon, Berlekamp [2] establish exponentially decreasing upper and lower bounds, respectively, on the error of the best codes for fixed code rates R smaller than the capacity for the standard channels (stationary finite alphabet channels without memory). These bounds happen to coincide up to the first order for rates near to the capacity. The authors of [2] regret that their proof of the lower bound cannot be extended to infinite alphabet channels or nonstationary channels because of the use of “fixed composition codes” (while the proofs of the upper estimate can be easily transferred to those channels). Changing parts of the proof in [2], we automatically obtain estimates of the same type as in [2] for the latter channels. Furthermore, as a matter of minor importance, we show that the order of coincidence of upper and lower bound for the high rates R can be rigorously improved." @default.
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- W2033757125 date "1969-01-01" @default.
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- W2033757125 title "Error estimates for low rate codes" @default.
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