Capacity and error probability in single-tone and multitone multiple access over an impulsive channel

Single-tone and multitone are two modulation methods which can combine multiple digital users over a single channel, and decode them independently, corresponding to time-division and frequency-division multiple access, respectively. When the channel noise is impulsive, its distribution at the receiver decision point, and therefore its effect on the users, depends strongly on the type of modulation. We quantify this effect using information theoretic measures: capacity and error-exponent, where the latter is represented by its cut-off rate parameter. For low to moderate impulse power, the cut-off rate associated with multitone is greater than the cut-off rate associated with single-tone-in contrast to the relation between the corresponding Shannon capacities. This leads to anomalous behavior of the error-versus-information-rate performance. We show that this behavior relates to the tendency toward Gaussianity of the noise after multitone demodulation. We also provide specific evaluation of this phenomena for advanced data transmission over the cable TV (hybrid fiber coax) channel.