Practical loss-resilient codes
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
New Sequences of Linear Time Erasure Codes Approaching the Channel Capacity
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Bounds on the number of iterations for turbo-like ensembles over the binary erasure channel
IEEE Transactions on Information Theory
Modern Coding Theory
Systematic design of low-density parity-check code ensembles for binary erasure channels
IEEE Transactions on Communications
Efficient erasure correcting codes
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Capacity-achieving sequences for the erasure channel
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Extrinsic information transfer functions: model and erasure channel properties
IEEE Transactions on Information Theory
Capacity-achieving ensembles for the binary erasure channel with bounded complexity
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On Convergence Speed of Capacity-Achieving Sequences for Erasure Channel
IEEE Transactions on Information Theory
Systematic design of low-density parity-check code ensembles for binary erasure channels
IEEE Transactions on Communications
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In this paper, new sequences (λn, ρn) of capacity achieving low-density parity-check (LDPC) code ensembles over the binary erasure channel (BEC) is introduced. These sequences include the existing sequences by Shokrollahi et al. as a special case. For a fixed code rate R, in the set of proposed sequences, Shokrollahi's sequences are superior to the rest of the set in that for any given value of n, their threshold is closer to the capacity upper bound 1 - R. For any given δ, 0 R, however, there are infinitely many sequences in the set that are superior to Shokrollahi's sequences in that for each of them, there exists an integer number n0, such that for any n n0, the sequence (λn, ρn) requires a smaller maximum variable node degree as well as a smaller number of constituent variable node degrees to achieve a threshold within δ-neighborhood of the capacity upper bound 1 - R. Moreover, it is proven that the check-regular subset of the proposed sequences are asymptotically quasi-optimal, i.e., their decoding complexity increases only logarithmically with the relative increase of the threshold. A stronger result on asymptotic optimality of some of the proposed sequences is also established.