Bounds on a probability for the heavy tailed distribution and the probability of deficient decoding in sequential decoding

摘要

Although sequential decoding of convolutional codes gives a very small decoding error probability, the overall reliability is limited by the probability P/sub G/ of deficient decoding, 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/sub 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/sub G/, that is, P/sub G/ /spl ap/ constant/spl times/1/(/spl sigma//sup /spl rho//N/sup /spl rho/-1/) for a large speed factor /spl sigma/ of the decoder and for a large receive buffer size N whenever the coding rate R and /spl rho/ satisfy E(/spl rho/)=/spl rho/R for 0 /spl les/ /spl rho/ /spl les/ 1.