On the rank of LDPC matrices constructed by Vandermonde matrices and RS codes
EM Gabidulin, M Bossert - 2006 IEEE International Symposium …, 2006 - ieeexplore.ieee.org
EM Gabidulin, M Bossert
2006 IEEE International Symposium on Information Theory, 2006•ieeexplore.ieee.orgWe calculate the rank of low-density parity-check (LDPC) matrices based on Vandermonde
matrix like constructions. In the case of prime fields the rank is given exactly. We show that
LDPC codes based on RS codes are a special case of the Vandermonde based
construction, thus also for these LDPC matrix construction, the rank calculation is valid.
However, for extension fields the calculation is more sophisticated because of the nilpotent
property of the parity check matrix. Therefore we can give presently only a bound for the rank …
matrix like constructions. In the case of prime fields the rank is given exactly. We show that
LDPC codes based on RS codes are a special case of the Vandermonde based
construction, thus also for these LDPC matrix construction, the rank calculation is valid.
However, for extension fields the calculation is more sophisticated because of the nilpotent
property of the parity check matrix. Therefore we can give presently only a bound for the rank …
We calculate the rank of low-density parity-check (LDPC) matrices based on Vandermonde matrix like constructions. In the case of prime fields the rank is given exactly. We show that LDPC codes based on RS codes are a special case of the Vandermonde based construction, thus also for these LDPC matrix construction, the rank calculation is valid. However, for extension fields the calculation is more sophisticated because of the nilpotent property of the parity check matrix. Therefore we can give presently only a bound for the rank in case of binary extension fields
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