Capacity and a lower bound to for a channel with symbol fission

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 lowerbound .