Zero-error capacity of a class of timing channels

Abstract

© 2014 IEEE. We analyze the problem of zero-error communication through timing channels that can be interpreted as discrete-time queues with bounded waiting times. The channel model includes the following assumptions: 1) time is slotted; 2) at most N particles are sent in each time slot; 3) every particle is delayed in the channel for a number of slots chosen randomly from the set {0, 1,K}) ; and 4) the particles are identical. It is shown that the zero-error capacity of this channel is log r , where \(r\) is the unique positive real root of the polynomial (xK+1-xK}-N\). Capacity-achieving codes are explicitly constructed, and a linear-time decoding algorithm for these codes devised. In the particular case \(N = 1 \) , \(K = 1 \) , the capacity is equal to log φ) , where φ = (1 + {5})/2 \) is the golden ratio, and constructed codes give another interpretation of the Fibonacci sequence.