Efficient Binomial Channel Capacity Computation with an Application to Molecular Communication

This paper develops an efficient method to compute the binomial channel capacity and applies it to the molecular channel. The binomial channel (with parameter n) takes the success probability for a Bernoulli trial as input and produces the number of successes in trials as output. The input alphabet is the unit interval and the output alphabet is the set of integers from zero to $n$. Despite the fact that the input alphabet is uncountably infinite the capacity-achieving input distributions turn out to have a small finite support that evolves gracefully as n increases. The ellipsoid algorithm was previously used to compute the binomial channel capacity, but convergence is rather slow even with a well-chosen initial condition. The Dynamic Assignment Blahut-Arimoto (DAB) algorithm starts with the capacity-achieving mass point locations for the n-1 case and exploits Csiszàr's Min-Max Capacity Theorem to check convergence and adjust mass point locations to achieve a much faster convergence rate, unlocking the potential for the capacity and corresponding input distribution to be computed for larger values of n.