DocumentCode :
2671072
Title :
Optimal Degree Distribution for LT Codes with Small Message Length
Author :
Hyytiä, Esa ; Tirronen, Tuomas ; Virtamo, Jorma
Author_Institution :
Norwegian Univ. of Sci. & Technol., Trondheim
fYear :
2007
fDate :
6-12 May 2007
Firstpage :
2576
Lastpage :
2580
Abstract :
Fountain codes provide an efficient way to transfer information over erasure channels. We give an exact performance analysis of a specific type of fountain codes, called LT codes, when the message length N is small. Two different approaches are developed. In a Markov chain approach the state space explosion, even with reduction based on permutation isomorphism, limits the analysis to very short messages, N < 4. An alternative combinatorial method allows recursive calculation of the probability of decoding after N received packets. The recursion can be solved symbolically for values of N < 10 and numerically up to N ap30. Examples of optimization results give insight into the nature of the problem. In particular, we argue that a few conditions are sufficient to define an almost optimal LT encoding.
Keywords :
Markov processes; channel coding; combinatorial mathematics; electronic messaging; iterative decoding; probability; LT codes; Markov chain approach; combinatorial method; erasure channels; fountain codes; iterative decoding; optimal degree distribution; permutation isomorphism; probability; recursive calculation; small message length; state space explosion; Communications Society; Councils; Encoding; Explosions; Iterative decoding; Laboratories; Performance analysis; Probability; Spraying; State-space methods;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
INFOCOM 2007. 26th IEEE International Conference on Computer Communications. IEEE
Conference_Location :
Anchorage, AK
ISSN :
0743-166X
Print_ISBN :
1-4244-1047-9
Type :
conf
DOI :
10.1109/INFCOM.2007.324
Filename :
4215906
Link To Document :
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