Optimal alphabet partitioning for semi-adaptive coding of sources of unknown sparse distributions

Practical applications that employ entropy coding for large alphabets often partition the alphabet set into two or more layers. Each symbol was encoded using suitable prefix coding for each layer. The problem of optimal alphabet partitioning was formulated for the design of a two layer semi-adaptive code and the given solution was based on dynamic programming. However, the complexity of the dynamic programming approach can be quite prohibitive for a long sequence and very large alphabet size. Hence, a simple greedy heuristic algorithm whose running time is linear in the number of symbols being encoded was given, irrespective of the underlying alphabet size. The given experimental results demonstrated the fact that superior prefix coding schemes for large alphabets can be designed using this approach as opposed to the typically ad-hoc partitioning approach applied in the literature.