Although sequential decoding of convolutional codes gives a very small decoding error probability, the overall reliability is limited by the probability P-G of deficientdecoding, the term introduced by Jelinek to ref...
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Although sequential decoding of convolutional codes gives a very small decoding error probability, the overall reliability is limited by the probability P-G of deficientdecoding, the term introduced by Jelinek to refer to decoding failures caused mainly by buffer overflow. The number of computational efforts in sequential decoding has the Pareto distribution and it is this "heavy tailed" distribution that characterizes P-G. The heavy tailed distribution appears in many fields and buffer overflow is a typical example of the behaviors in which the heavy tailed distribution plays an important role. In this paper, we give a new bound on a probability in the tail of the heavy tailed distribution and, using the bound, prove the long-standing conjecture on P-G, that is, P-G approximate to constant x 1/(sigma(rho) Nrho-1) for a large speed factor sigma of the decoder and for a large receive buffer size N whenever the coding rate R and rho satisfy E(rho) = rhoR for 0 less than or equal to p less than or equal to 1.
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