A New Code for Encoding All Monotone Sources With a Fixed Large Alphabet Size

The problem of designing a fixed code for encoding all monotone sources with a large alphabet size n is studied. It is proved that if the code-lengths of a code sequence are of order O(log n), then the redundancy for almost all monotone sources with n symbols is very close to that for a specific distribution, so-called average distribution. Noting this point, for any large alphabet size n, a new code with a very simple structure is proposed whose redundancy is close to that of the Huffman code for almost all monotone sources with alphabet size n.