Binary Combinatorial Coding

We present a novel binary entropy code called combinatorial coding (CC). The theoretical basis for CC has been described previously under the context of universal coding [1], enumerative coding [2], and minimum description length [3]. The code described in these references works as follows: assume the source data of length M is binary, memoryless, and generated with an unknown parameter θ, the probability that a “1” occurs. To code the data, count the number of “1”s k and encode this using log( 1) M +     bits. Next, use a ranking algorithm [4] to compute the index of the data in a lexicographic listing of all binary sequences of length M with k “1”s. There are C( , ) M k such sequences so the index can be transmitted with logC( , ) M k     bits. In general, ranking an M-bit block requires M-bit integer addition and storage. On today’s 32-bit computer architectures, 32 M = is a practical limitation on block size.