Blahut Arimoto algorithm

An implementation in Python3 of the standard convex optimization technique by Arimoto and Blahut.
The script is intended to approximate the channel capacity C for a discrete memoryless channel (DMC) given a stationary transition probability distribution trans_prob_distr as a two dimensional array, n x m matrix.

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Description of algorithm

Given a fixed transition probability distribution $\omega_{ij}$ for the DMC, first initialize a vector $p^{0}=(p_1,p_2,...)$, where $p_i \ge 0$ and $\sum_np_i=1$, and where $0\le i\le n$ and $0\le j\le m$.
Then do for iterations $t=(1,2,...)$:

1. Evolve Q:
   $Q_{ji}^{t} = \frac{p_i^{t-1}\omega_{ij}}{\sum_{k=1}^n p_k^{t-1} \omega_{kj}}$
2. Evolve p:
   $p_i^{t} = \frac{\prod_{j=1}^m (Q_{ji}^t)^{\omega_{ij}}}{\sum_{k=1}^n \prod_{j=1}^m (Q_{jk}^t){\omega_{kj}}}$

As long as the criteria for convergence are satisfied, the channel capacity can be approximated to arbitrary accuracy by the equation:
$\lim_{t\rightarrow\infty} \sum_{i=1}^n \sum_{j=1}^m p_i^t \omega_{ij} \log_2 \Big (\frac{Q_{ji}^t}{p_i^t}\Big )$

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To run:

Change the transition probability distribution and increase number_of_iterations to achieve satisfactory accuracy.