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Paper IPM / M / 16480  


Abstract:  
LDPC codes based on affine permutation matrices,
APMLDPC codes, have been attracted recently, because of some
advantages rather than QCLDPC codes in minimumdistance,
cycle distribution and errorrate performance. In this paper,
circulant and anticirculant permutation matrices are used to
define a class of LDPC codes, called AQCLDPC codes, which
can be considered as an especial case of APMLDPC codes. In
fact, each AQCLDPC code can be verified by a sign matrix and
a slope matrix which are helpful to show each cycle in the Tanner
graph by a modular linear equation. For the normal sign matrix
A, if ï¿½??1 2 A, it is shown that the corresponding AQCLDPC
code has maximumgirth 8. Finally, two explicit constructions
for AQCLDPC codes with girths 6, 8 are presented which have
some benefits rather than the explicitly constructed QC and APM
LDPC codes in minimumdistance, cycle distributions and biterrorrate performances.
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