Analysis of the Second Moment of the LT Decoder

We analyze the second moment of the ripple size during the LT decoding process and prove that the standard deviation of the ripple size for an LT-code with length k is of the order of root k. Together with a result by Karp et. al (2004) stating that the expectation of the ripple size is of the order of k, this gives bounds on the error probability of the LT decoder. We also give an analytic expression for the variance of the ripple size up to terms of constant order, and refine the expression of Karp et. al for the expectation of the ripple size up to terms of the order of 1/k, thus providing a first step towards an analytic finite-length analysis of LT decoding.

Published in:
2009 Ieee International Symposium On Information Theory, Vols 1- 4, 2326-2330
Presented at:
IEEE International Symposium on Information Theory (ISIT 2009), Seoul, SOUTH KOREA, Jun 28-Jul 03, 2009
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa

 Record created 2010-11-30, last modified 2018-03-17

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