Alphabet Partitioning Techniques for Semi-Adaptive Huffman Coding of Large Alphabets Alphabet Partitioning Techniques for Semi-Adaptive 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 semi-adaptive 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 A preliminary version of this paper appeared in Proc. IEEE Data Compression Conference (DCC ’03), pp. 372-381, March 2003. [email protected]. Research supported by NSF Grant CCF-0118915. [email protected]. Research supported in part by NSF Grant CCF-0118915, NSF CAREER Grant CCF-0093373, and NSF Grant CCF-0541255. [email protected]. Research supported in part by NSF Grant CCF-0118915 and NSF Grant CCF-0208678. [email protected]. Research supported in part by NSF Grant CCF-0208678.