Two-Part Codes with Low Worst-Case Redundancies for Distributed Compression of Bernoulli Sequences

Rissanen's lower bound on the worst- case redundancy over the maximum likelihood (ML) coding length was obtained by analyzing the perfor- mance of two-part codes. We consider a class of particularly simple two-part codes for Bernoulli se- quences that quantize the ML parameter estimate into one of K bins, describe that bin with log2(K) bits, and encode the input sequence according to the quan- tized parameter estimate. In addition to their sim- ple structure, these codes have an appealing applica- tion to universal distributed lossless source coding of Bernoulli sequences. We propose several schemes for quantizing the parameter estimate; the best worst- case redundancy for the entire sequence attainable in our class of codes is 1.047 bits above Rissanen's bound. quence x as n0(x) and n1(x), so n0(x) , P N=1 1{xi=0} and n1(x) , PN=1 1{xi=1} = N n0(x), where 1{·} denotes an