A variable-length source coding theorem for correlated information sources

A variable-length source coding theorem is proved for a pair of discrete memoryless correlated information sources. The average length of codewords per source letter for source X provided the side information Y is bounded below by the conditional entropy H(X|Y) and above by the same entropy plus J/L where L is the number of source letters encoded and J is the size of ensemble Y. The Huffman encoding procedure is also generalized for this case.