Capacity of a Burst-Noise Channel

In information theory the symmetric binary channel is the classical model of a noisy binary channel. This channel generates a sequence of binary noise digits z n , which it adds (modulo 2) to input digits x n to produce output digits y n = x,, + z n . The symmetric binary channel is memoryless; a sequence of independent trials produces the noise digits z n . Each trial has the same probability P( 1) of producing an error and probability 1 -- P( 1) = P ( 0 ) of no error. The capacity C(sym. bin.) of this channel is well known (see Shannon 1 ): C(sym. bin.) = 1 + P ( 0 ) log2 P ( 0 ) + P( 1) logo P( 1). Channels with memory occur in practice. If radio static or switching transients produce the noise, the errors group into isolated bursts (several errors close together). Independent trials fail to simulate such a burst-noise. Section II of this paper presents a model of a burst-noise channel that is simple enough to permit calculation of the channel capacity C (see Sections III and VI). Sections IV and V give run distributions, the covariance function and other probability formulas as aids to 1253