On the redundancy of optimum fixed-to-variable length codes

There has been much interest in recent years in bounds on the redundancy of Huffman codes, given only partial information about the source word distribution, such as the probability of the most likely source. This work determines upper and lower bounds for the redundancy of Huffman codes of source words which are binomially distributed. Since the complete distribution is known, it is possible to determine bounds which are much tighter than other bounds in the literature, given only p, the probability of the most likely symbol of the binary source, and K, where there are 2^K source words. The upper and lower bounds will be shown to converge to the same value as K becomes large, resulting in a simple approximation which can be used to predict the redundancy of the Huffman code, given p and K, without constructing the code