A Tree Based Algorithm for Generating All Possible Binary Compact Codes with N Codewords

Mohammadali KHOSRAVIFARD  Morteza ESMAEILI  Hossein SAIDI  T. Aaron GULLIVER  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.10   pp.2510-2516
Publication Date: 2003/10/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Source Coding/Image Processing
Keyword: 
binary compact code,  Huffman code,  complete binary tree,  

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Summary: 
A source code for N symbols can be represented by a codeword length sequence (1,2,,N). A binary code is compact if it satisfies = 1. Also we may assume that 1 1 2 N. In this paper, we show that these two constraints can be replaced by max i for 1 i N - 1. Using the latter characterization, we construct a tree T N representing all binary compact codes. In fact every leaf of T N represents a compact code and vice versa. This technique can also be used to generate all compact codes for a given (1,2,,k), k < N.