A measure of efficiency for a class of decision feedback communication systems

• Published in: Journal of the Franklin Institute 1968-01, Vol.285 (3), p.175-186
• Main Authors: Mulholland, R.G., Joshi, A.K., Chu, J.T.
• Format: Article
• Language: English
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/0016-0032(68)90447-X

A measure of efficiency is introduced for a broad class of decision feedback communication systems in which the feedback channel is noiseless and both the source and the forward channel are discrete and memoryless. The proposed measure R, which can be interpreted as a transmission rate, is a non-negative number that never exceeds the transmission rate Ro that can be achieved with the source and forward channel without the aid of feedback. However, there does exist a necessary and sufficient condition for which R = R o. Roughly speaking, this condition is that requests for retransmission are made only when signals received in the past fail to impart any information as to which message symbol has been selected at the source. The measure R also has the property that it vanishes if, and only if, the rate R o vanishes. In other words, the measure R reflects the idea that it is possible to convey information from source to receiver using feedback if, and only if, the forward channel is capable of carrying information without the aid of feedback.