Abstract:
For a given finite set of messages and their assigned probabilities, Huffman's procedure gives a method of computing a length set (a set of codeword lengths) that is opti...Show MoreMetadata
Abstract:
For a given finite set of messages and their assigned probabilities, Huffman's procedure gives a method of computing a length set (a set of codeword lengths) that is optimal in the sense that the average word length is minimized. Corresponding to a particular length set, however, there may be more than one code. LetL(n)consist of all length sets with largest termn, and, for any\ell \in L(n), let{\cal S}( \ell)be the smallest number of states in any finite-state acceptor which accepts a set of codewords with length set\ell. It is shown that, for alln > 1,n^{2}/(16 \log_{2} n) \leq max {\cal S}(\ell) \leq 0(n^{2}).\ell \in L(n)
Published in: IEEE Transactions on Information Theory ( Volume: 22, Issue: 3, May 1976)