Lossless Source Codes for a Class Described by Variational Distance and Optimal Merging Algorithm

This paper considers lossless uniquely decodable source codes for a class of distributions described by a ball with respect to the total variational distance, centered at a nominal distribution with a given radius. The coding problem is formulated using minimax techniques, in which the maximum of the average codeword length over the class of distributions is minimized subject to Kraft inequality. Firstly, the maximization over the class of distributions is characterized resulting in an equivalent pay-off. consisting of the maximum and minimum codeword length and the average codeword length with respect to the nominal distribution. Secondly, an algorithm is introduced which computes the optimal weight vector as a function of the class radius. Finally, the optimal codeword length vector is found as a function of the weight vector.