Alphabet partitioning techniques for semiadaptive Huffman coding of large alphabets

Practical applications that employ entropy coding for large alphabets often partition the alphabet set into two or more layers, and encode each symbol by using some suitable prefix coding for each layer. In this paper, we formulate the problem of finding an alphabet partitioning for the design of a two-layer semiadaptive code as an optimization problem, and give a solution based on dynamic programming. However, the complexity of the dynamic programming approach can be quite prohibitive for a long sequence and a very large alphabet size. Hence, we also give a simple greedy heuristic algorithm whose running time is linear in the length of the input sequence, irrespective of the underlying alphabet size. Although our dynamic programming and greedy algorithms do not provide a globally optimal solution for the alphabet partitioning problem, experimental results demonstrate that superior prefix coding schemes for large alphabets can be designed using our new approach.