Tight bounds on the redundancy of Huffman codes

  • Authors:
  • D. Manstetten

  • Affiliations:
  • Lehrstuhl fuer Angewandte Math. Insbesondere Inf., RWTH Aachen

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

A method for deriving optimal upper bounds on the redundancy of binary Huffman codes in terms of the probability p1 of the most likely source letter is presented. This method will be used to compute bounds for all p1⩾1/127, which were previously known only for a few special cases. Furthermore, the known optimal lower bound for binary Huffman codes is generalized to arbitrary code alphabets and some upper bounds for D-ary Huffman codes, 2⩽D<∞, are given, which are the tightest possible for all p1⩾1/2