A Graph-Based Approach to the Computation of Rate-Distortion and Capacity-Cost Functions with Side Information

We consider the point-to-point lossy coding for computing and channel coding problems with two-sided information. We first unify these problems by considering a new generalized problem. Then we develop graph-based characterizations and derive interesting reductions through explicit graph operations, which reduce the number of decision variables. After that, we design alternating optimization algorithms for the unified problems, so that numerical computations for both the source and channel problems are covered. With the help of extra root-finding techniques, proper multiplier update strategies are developed. Thus our algorithms can compute the problems for a given distortion or cost constraint and the convergence can be proved. Also, extra heuristic deflation techniques are introduced which largely reduce the computational time. Numerical results show the accuracy and efficiency of our algorithms.