Coding of Sets of Words

We study the problem of coding of unordered sets of words, appearing in natural language processing, retrieval, machine learning, computer vision, and other fields. We note that this problem is different from the problem of coding of a particular sequence of same words, and show that up to log(m!) bits (where m is the number of words in the set) can be saved by specialized codes for sets. We propose one possible design of such codes, and prove its asymptotic optimality in the memoryless model.