Good Codes Based on Very Sparse Matrices
Proceedings of the 5th IMA Conference on Cryptography and Coding
Codes from zero-divisors and units in group rings
International Journal of Information and Coding Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
On algebraic construction of Gallager and circulant low-density parity-check codes
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
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An algebraic group ring method for constructing codes with no short cycles in the check matrix is derived. It is shown that the matrix of a group ring element has no short cycles if and only if the collection of group differences of this element has no repeats. When the method is applied to elements in the group ring with small support this gives a general method for constructing and analysing low density parity check (LDPC) codes with no short cycles from group rings. Examples of LDPC codes with no short cycles are constructed from group ring elements and these are simulated and compared with known LDPC codes, including those adopted for wireless standards.