Bounds on the redundancy of Huffman codes
IEEE Transactions on Information Theory
On the average codeword length of optimal binary codes for extended sources
IEEE Transactions on Information Theory
On the redundancy of optimal binary prefix-condition codes for finite and infinite sources
IEEE Transactions on Information Theory
On the redundancy achieved by Huffman codes
Information Sciences: an International Journal
New bounds on D-ary optimal codes
Information Processing Letters
An efficient compression code for text databases
ECIR'03 Proceedings of the 25th European conference on IR research
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The problem of providing bounds on the redundancy of an optimal codefor a discrete memoryless source in terms of the probability distribution ofthe source, has been extensively studied in the literature. The attentionhas mainly focused on binary codes for the case when the most or the leastlikely source letter probabilities are known. In this paper we analyze therelationships among tight lower bounds on the redundancy r. Let r ≥&phis;_D,i(x) be the tight lower bound on r for D-ary codes interms of the value x of the i-th most likely source letter probability. Weprove that &phis;_D,i-1(x) ≤ &phis;_D,i(x) forall possible x and i. As a consequence, we can bound the redundancy whenonly the value of a probability (but not its rank) is known. Anotherconsequence is a shorter and simpler proof of a known bound. We also providesome other properties of tight lower bounds. Finally, we determine anachievable lower bound on r in terms of the least likely source letterprobability for D ≥ 3, generalizing the known bound for the case D =2.