2009/02/18 by Ghid Maatouk, Maatouk, Ghid, Amin Shokrollahi +1
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.0902.3114
openalex publication_date 2009/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 √ k. Together with a result by Karp et. al stating that the expectation of the ripple size is of the order of k [3], 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 in [3] 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.