Higher Order Context Transformations

The context transformation and generalized context transformation methods, we introduced recently, were able to reduce zero order entropy by exchanging digrams, and as a consequence, they were removing mutual information between consecutive symbols of the input message. These transformations were intended to be used as a preprocessor for zero-order entropy coding algorithms like Arithmetic or Huffman coding, since we know, that especially Arithmetic coding can achieve a compression rate almost of the size of Shannon’s entropy. This paper introduces a novel algorithm based on the concept of generalized context transformation, that allows transformation of words longer than simple digrams. The higher order contexts are exploited using recursive form of a generalized context transformation. It is shown that the zero order entropy of transformed data drops significantly, but on the other hand, the overhead given by a description of individual transformations increases and it has become a limiting factor in a successful transformation of smaller files.