Low-Memory Adaptive Prefix Coding

In this paper we study the adaptive prefix coding problem in cases where the size of the input alphabet is large. We present an online prefix coding algorithm that uses O(sigma^{1/lambda+epsiv}) bits of space for any constants epsiv > 0, > 1, and encodes the string of symbols in O(loglog sigma) time per symbol in the worst case, where sigma is the size of the alphabet. The upper bound on the encoding length is lambdanH(s) + (lambda/ ln 2 + 2 + epsiv)n + O(sigma^1/lambda log² sigma) bits.