LOSSLESS COMPRESSION AND ALPHABET SIZE by DANIEL

Lossless data compression through exploiting redundancy in a sequence of symbols is a well-studied field in computer science and information theory. One way to achieve compression is to statistically model the data and estimate model parameters. In practice, most general purpose data compression algorithms model the data as stationary sequences of 8-bit symbols. While this model fits very well the currently used computer architectures and the vast majority of information representation standards, other models may have both computational and information theoretic merits in being more efficient in implementation or fitting some data closer. In addition, compression algorithms based on the 8 bit symbol model perform very poorly on data represented by binary sequences not aligned with byte boundaries either because the fixed symbol length is not a multiple of 8 bits (e.g. DNA sequences) or because the symbols of the source are encoded into bit sequences of variable length. Throughout this thesis, we assume that the source alphabet consists of blocks of equal size of elementary symbols (typically bits), and address the impact of this block size on lossless compression algorithms in general and in the context of socalled block-sorting compression algorithms in particular. These algorithms are quite popular both in theory and in practice and are the subjects of intensive research with many interesting results in recent years. We show that compression on the bit level is tolerant to sources that are not aligned to byte boundaries, while performing reasonably well for byte-aligned sources.