Capacity and a lower bound toR_{mbox{comp}}for a channel with symbol fission
R. Dick, T. Berger · IEEE Transactions on Information Theory · 1976
We derive sequences of upper and lower bounds that converge to the capacity of a binary channel in which a one takes twice as long to send as does a zero and may be received either as a one or as a pair of zeros. Such a fission mechanism can occur, for example, in the use of Morse code over a noisy channel. Next we present a sequential decoding algorithm for the channel which is particularly easy to implement. By means of the Perron-Frobenius theorem and an extension of Zigangirov's analysis of sequential decoding, we overbound error probability and thereby again underbound capacity. The resulting lower bound turns out to be within 0.014 nats of the fourteenth-order upper bound to capacity, uniformly in the fission probability. By extending an analytical method due in part to Jelinek, we overbound expected decoding computation and thereby lowerboundR_{comp}.