Universal lossless data compression with side information by using a conditional MPM grammar transform

The MPM (multilevel pattern matching) grammar transform underlies a lossless data compression algorithm developed by Kieffer, Yang, Nelson and Cosman (see IEEE Trans. on Inform. Theory, 2000. In this paper, we extend the MPM grammar transform to the case of side information known to both the encoder and decoder, yielding a conditional MPM grammar transform which is referred to as the CMPM (r,I) transform. Based on the CMPM (r,I) transform, we develop a universal lossless data compression algorithm with side information called the CMPM algorithm, which has linear time and storage complexity and asymptotically achieves the conditional entropy rate of any stationary, ergodic source pair. The advantage of using side information, if any, for data compression is obvious; one can considerably reduce the compression rate if the side information is highly correlated with a sequence to be compressed