Detection and Information Rate of Telegraphic Signals

"Detection" in the title of this paper is used in the sense of decision-making, rather than demodulation. The ideal communication rate for a physical channel is provided by Shannon's formula
C \leq W \log(1 + P/N)
, and for a binary symmetric channel the theoretical amount of information per digit is
I = 1 + p log p + q log q
, where
p
is probability of error per digit and
p + q = 1
. Various error-correcting codes are compared with the second formula. It is shown that correlation-detection is equivalent to minimum-distance detection provided all code groups are of equal mean power, and that a binary-coded signal can always be adjusted to the constant-power state. Experimental results are reported on error reduction in a two-out-of-five code by the use of correlation detection. It is noted that square-law detection would be inferior to linear detection in such a system.