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arXiv · 1111.1432

Universal Lossless Data Compression Via Binary Decision Diagrams

J. Kieffer·P. Flajolet·E. -h. Yang
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Abstract

A binary string of length $2^k$ induces the Boolean function of $k$ variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The given binary string is fully recoverable from this ROBDD. We exhibit a lossless data compression algorithm in which a binary string of length a power of two is compressed via compression of the ROBDD associated to it as described above. We show that when binary strings of length $n$ a power of two are compressed via this algorithm, the maximal pointwise redundancy/sample with respect to any s-state binary information source has the upper bound $(4\log_2s+16+o(1))/\log_2n $. To establish this result, we exploit a result of Liaw and Lin stating that the ROBDD representation of a Boolean function of $k$ variables contains a number of vertices on the order of $(2+o(1))2^{k}/k$.

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J. Kieffer, P. Flajolet, E. -h. Yang. 2011-11-06. Universal Lossless Data Compression Via Binary Decision Diagrams. https://arxiv.org/abs/1111.1432

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