Practical loss-resilient codes
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Good Codes Based on Very Sparse Matrices
Proceedings of the 5th IMA Conference on Cryptography and Coding
Error Control Coding, Second Edition
Error Control Coding, Second Edition
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Low-complexity high-speed decoder design for quasi-cyclic LDPC codes
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A lattice-based systematic recursive construction of quasi-cyclic LDPC codes
IEEE Transactions on Communications
A link between quasi-cyclic codes and convolutional codes
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Combinatorial constructions of low-density parity-check codes for iterative decoding
IEEE Transactions on Information Theory
On algebraic construction of Gallager and circulant low-density parity-check codes
IEEE Transactions on Information Theory
Quasicyclic low-density parity-check codes from circulant permutation matrices
IEEE Transactions on Information Theory
LDPC block and convolutional codes based on circulant matrices
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Quasi-cyclic LDPC codes for fast encoding
IEEE Transactions on Information Theory
Algebraic construction of sparse matrices with large girth
IEEE Transactions on Information Theory
A lattice-based systematic recursive construction of quasi-cyclic LDPC codes
IEEE Transactions on Communications
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Four classes of maximum-girth geometrically structured column-weight-two regular quasi-cyclic (QC) low-density parity-check (LDPC) codes are introduced. Two classes of these codes, referred to as Type-I and Type-II codes, are with row-weights 4 and 3, and maximum girths 16 and 24, respectively. The idea behind the construction of these two classes of codes, with rates at least 1/2 and 1/3, is slightly generalized to obtain two classes of variable-high-rate codes, referred to as Type-III1 and Type-III2 codes, with maximum girth 20 and 16, respectively. A low-complexity deterministic algorithm for constructing these four classes of codes is given. The algorithm generates maximum-girth Type-I and Type-II codes with almost arbitrary length n not less than 216 and 243, respectively. The output of the algorithm substantially improves on some of the previously best known codes constructed using a randomized progressive edge-growth (RPEG) algorithm. For instance, we have rate-0.71 Type-III1 codes of lengths 308 and 728 with girths 10 and 12, respectively, versus the code lengths 385 and 840 obtained by the RPEG algorithm. Simulation results on AWGN channel confirm that, from BER performance perspective, the constructed LDPC codes are superior to the column-weight-two LDPC codes constructed by the previously reported methods. The generator matrix G(D) of the convolutional codes associated with Type-I and Type-II codes is given. The free distance dfree of such a convolutional code is equal to the minimum distance of the corresponding QC block code.