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Low-Density Parity-Check Codes from Transversal Designs with Improved Stopping Set Distributions

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2 Author(s)
Alexander Gruner ; Wilhelm Schickard Institute for Computer Science, Eberhard Karls Universitat Tubingen, Sand 13, D-72076 Tubingen, Germany ; Michael Huber

This paper examines the construction of low-density parity-check (LDPC) codes from transversal designs based on sets of mutually orthogonal Latin squares (MOLS). By transferring the concept of configurations in combinatorial designs to the level of Latin squares, we thoroughly investigate the occurrence and avoidance of stopping sets for the arising codes. Stopping sets are known to determine the decoding performance over the binary erasure channel and should be avoided for small sizes. Based on large sets of simple-structured MOLS, we derive powerful constraints for the choice of suitable subsets, leading to improved stopping set distributions for the corresponding codes. We focus on LDPC codes with column weight 4, but the results are also applicable for the construction of codes with higher column weights. Finally, we show that a subclass of the presented codes has quasi-cyclic structure which allows low-complexity encoding.

Published in:

IEEE Transactions on Communications  (Volume:61 ,  Issue: 6 )