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A Universal Grammar-Based Code for Lossless Compression of Binary Trees

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3 Author(s)
Jie Zhang ; Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada ; En-Hui Yang ; John C. Kieffer

We consider the problem of lossless compression of binary trees, with the aim of reducing the number of code bits needed to store or transmit such trees. A lossless grammar-based code is presented, which encodes each binary tree into a binary codeword in two steps. In the first step, the tree is transformed into a context-free grammar from which the tree can be reconstructed. In the second step, the context-free grammar is encoded into a binary codeword. The decoder of the grammar-based code decodes the original tree from its codeword by reversing the two encoding steps. It is shown that the resulting grammar-based binary tree compression code is a universal code on a family of probabilistic binary tree source models satisfying certain weak restrictions.

Published in:

IEEE Transactions on Information Theory  (Volume:60 ,  Issue: 3 )