Expander ℓ0-Decoding
نویسندگان
چکیده
منابع مشابه
Low-Density Parity-Check Codes: Constructions and Bounds
Low-density parity-check (LDPC) codes were introduced in 1962, but were almost forgotten. The introduction of turbo-codes in 1993 was a real breakthrough in communication theory and practice, due to their practical effectiveness. Subsequently, the connections between LDPC and turbo codes were considered, and it was shown that the latter can be described in the framework of LDPC codes. In recent...
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We show that expander codes attain the capacity of the binary-symmetric channel under iterative decoding. The error probability has a positive exponent for all rates between zero and channel capacity. The decoding complexity grows linearly with code length.
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Four different ways of obtaining low-density parity-check codes from expander graphs are considered. For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived. These bounds are compared with the known eigenvalue-based lower bounds on the minimum distance of expander codes. Furthermore, Tanner’s parity-oriented eigenva...
متن کاملLP decoding of expander codes: a simpler proof
A code C ⊆ Fn 2 is a (c, ǫ, δ)-expander code if it has a Tanner graph, where every variable node has degree c, and every subset of variable nodes L0 such that |L0| ≤ δn has at least ǫc|L0| neighbors. Feldman et al. (IEEE IT, 2007) proved that LP decoding corrects 3ǫ−2 2ǫ−1 · (δn − 1) errors of (c, ǫ, δ)expander code, where ǫ > 2 3 + 1 3c . In this paper, we provide a simpler proof of their resu...
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In this paper we investigate the structure of the fundamental polytope used in the Linear Programming decoding introduced by Feldman, Karger and Wainwright. We begin by showing that for expander codes, every fractional pseudocodeword always has at least a constant fraction of non-integral bits. We then prove that for expander codes, the active set of any fractional pseudocodeword is smaller by ...
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ورودعنوان ژورنال:
- CoRR
دوره abs/1508.01256 شماره
صفحات -
تاریخ انتشار 2015