A scalable entropy code

Summary form only given. We present an algorithm for constructing entropy codes that allow progressive transmission. The algorithm constructs codes by forming an unbalanced tree in a similar to fashion to Huffman coding. It differs, however, in that nodes are combined in a rate-distortion sense. Because nodes are formed with both rate and distortion in mind, each internal tree node, in addition to each leaf node, has a reconstruction vector and a path map, or codeword, associated with it. The code associated with the leaf nodes is a lossless, asymptotically optimal (for many sources), prefix code. The codes associated with internal nodes are lossy prefix codes, but have lower average length than the lossless code. Using codes associated with the tree and pruned subtrees, an encoded source can be reconstructed with higher fidelity as more bits become available therefore allowing a successive approximation character. In addition, because the lossless code is asymptotically optimal for many sources, the the cost of using the lossless progressive code can be made arbitrarily small for these sources.