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Doubly-Generalized LDPC Codes: Stability Bound Over the BEC

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3 Author(s)
Paolini, E. ; DEIS/WiLAB, Univ. of Bologna, Cesena ; Fossorier, M.P.C. ; Chiani, M.

The iterative decoding threshold of low-density parity-check (LDPC) codes over the binary erasure channel (BEC) fulfills an upper bound depending only on the variable and check nodes with minimum distance 2. This bound is a consequence of the stability condition, and is here referred to as stability bound. In this paper, a stability bound over the BEC is developed for doubly-generalized LDPC codes, where variable and check nodes can be generic linear block codes, assuming maximum a posteriori erasure correction at each node. It is proved that also in this generalized context the bound depends only on the variable and check component codes with minimum distance 2. A condition is also developed, namely, the derivative matching condition, under which the bound is achieved with equality. The stability bound leads to consider single parity-check codes used as variable nodes as an appealing option to overcome common problems created by generalized check nodes.

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Information Theory, IEEE Transactions on  (Volume:55 ,  Issue: 3 )