Grouping algorithm for lossless data compression

Summary form only given. There are in fact two main parts in this paper. One is a modification to context-tree weighting algorithm known as CTW, and the other is a new algorithm called grouping. In the CTW method, we consider a binary tree as a context-tree T_D, where each node s in this tree has length l(s) with 0⩾l(s)⩾D for a source generating a sequence of binary digits. There are counts a_s , and b_s, for each node s of T_D denoting the number of zeros and ones respectively. Each internal node s of the tree has two children 0s and 1s. The root of the tree corresponds to memoryless model λ and each node corresponds to a prefix sequence. The second part of the paper, introduces a new algorithm that considers all different binary trees of length ⩾D as complete sets of alphabets for a binary source. By using the KT estimator for each of these alphabet models, we find the probability distribution gained by all different complete extended alphabets. By grouping these models, we define the coding distribution as the average of the probabilities for all the models. We have demonstrated a quick algorithm for this idea and call this approach a grouping algorithm. This approach also breaks the extended alphabet model probability distribution into the non-extended one. Note that the result of this algorithm will produce at most log M(D) more code words than the optimal selection of strings of length at most D, as letters of the alphabet