On the expected codeword length per symbol of optimal prefix codes for extended sources
Author: 
Jay ChengAuthors Info & Claims
Pages 325 - 328
Abstract
For a discrete memoryless source X, it is well known that the expected codeword length per symbol Ln(X) of an optimal prefix code for the extended source Xn converges to the source entropy. However, the sequence Ln(X) need not be nonincreasing. As the encoding and decoding complexity increases exponentially with the block length, from a practical perspective it is both important and of interest to know when we can have a decrease in the expected codeword length per symbol by increasing the block length.
In this paper, we obtain some results on the behavior of Ln(X) and provide sufficient conditions for Lkn(X)< Ln(X) in terms of k, n, the probability of the most likely source symbol p1 and/or the minimum codeword length of an optimal code for the original source. By using these sufficient conditions, for any given n ≥ 1 and non-dyadic pn<over>1, we also obtain an integer k* ≥ 2 such that Lk'n(X) < Ln(X) for all k' ≥ k*. Our results could be regarded as extensions and generalizations of those by Montgomery and Kumar.
References
[1]
C. E. Shannon, "A mathematical theory of communication," Bell System Technical Journal, vol. 27, pp. 379--423 (Part I), 623--656 (Part II), July, October 1948.
[2]
T. M. Cover and J. A. Thomas, Elements of Information Theory, New York, NY: John Wiley & Sons, 1991.
[3]
B. L. Montgomery and B. V. K. V. Kumar, "On the average codeword length of optimal binary codes for extended sources," IEEE Transactions on Information Theory, vol. 33, pp. 293--296, March 1987.
[4]
P. M. Fenwick, "Huffman code efficiencies for extentions of sources," IEEE Transactions on Communications Theory, vol. 43, pp. 163--165, February/March/April 1995.
[5]
R. M. Capocelli and A. De Santis, "A note on D-ary Huffman codes," IEEE Transactions on Information Theory, vol. 37, pp. 174--179, January 1991.
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- On the expected codeword length per symbol of optimal prefix codes for extended sources
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Published In
August 2007
716 pages
ISBN:9781595936950
DOI:10.1145/1280940
- General Chairs:
- Mohsen Guizani,
- Hsiao-Hwa Chen,
- Program Chair:
- Xi Zhang
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Published: 12 August 2007
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IWCMC07: International Wireless Communications and Mobile Computing Conference
August 12 - 16, 2007
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