Universal Lossless Data Compression Via Binary Decision Diagrams

A binary string of length 2 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 log2 s+16+o(1))= log2 n. 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.