On the capacity of a band-limited channel perturbed by statistically dependent interference

If is the greatest rate at which information can be reliably conveyed through a channel of bandwidth that accel)ts signals of average power no greater than , adding to them white Gaussian noise of average power and interference of average power no greater than which may depend on the signal being transmitted and on all of the other signals in the code book, then begin{equation} C leq W log P/2J qquad qquad for P geq 2J end{equation} and begin{equation} C = 0 qquad qquad qquad for P leq 2J. end{equation} If begin{equation} C_1= begin{cases} W log P^2 /4J(P- J)& for P geq 2J\\ 0& for P leq 2J end{cases} end{equation} and begin{equation} C_2= begin{cases} W log P/(J + N)& for P geq (J + N)^2 /J\\ W log (1 + (sqrt{P} - sqrt{J})^2 /N)& for J leq P leq (J+N)^2/J\\ 0& for P leq J. end{cases} end{equation} then, when , begin{equation} C_1 leq C leq C_2. end{equation} When , the maximum rate of reliable communication becomes , which is attained by the use of randomly-selected white Gaussian noise-like signals.