Duality relationships for rate-distortion problems

This work formulates a procedure of obtaining Lagrangian dual problems to a class of rate-distortion problems. The technique used here is analogous to the techniques used to address channel capacity problems in Vishwanath et al. (2003). The dual problem now obtained is a maximization problem and its solution in general a lower bound to the rate-distortion problem. This dual problem provides us with simple lower bounds to the rate achievable under distortion constraints, and with algorithms to compute this rate. We combine this dual problem with that obtained for channel capacity in Vishwanath et al. to obtain upper and lower bounds to worst-case channel capacity and worst-case rate under distortion constraints problems.