On a class of multilevel universal source coding schemes

This work seeks to reduce the computational complexity and the coding rate associated with a class of universal source coding schemes for encoding fixed length m-ary sequences into variable length sequences. The Lynch-Davisson (1966) minimax universal source coding scheme, the Tanaka-Ando-Leon-Garcia (TAL) weighted universal source coding scheme (1985), and Cover´s general enumerative source coding scheme (1973) are modified. The essence of the proposed modification is to rename the m symbols of the alphabet so that the most frequent symbol of the given input data block will be denoted 0 the second most frequent symbol will be denoted 1, and so on, until the least frequent symbol will be denoted m-1. It is proven that out of all the m permutations of the m symbols, the proposed one minimizes the computational complexity of the above mentioned schemes, and preserves their unique decodability property. Moreover, for the modified TAL scheme it is proven that for block lengths n≫m further data compression can be achieved