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| Paper IPM / M / 16480 |
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| Abstract: | |
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LDPC codes based on affine permutation matrices,
APM-LDPC codes, have been attracted recently, because of some
advantages rather than QC-LDPC codes in minimum-distance,
cycle distribution and error-rate performance. In this paper,
circulant and anti-circulant permutation matrices are used to
define a class of LDPC codes, called AQC-LDPC codes, which
can be considered as an especial case of APM-LDPC codes. In
fact, each AQC-LDPC 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 �??1 2 A, it is shown that the corresponding AQC-LDPC
code has maximum-girth 8. Finally, two explicit constructions
for AQC-LDPC codes with girths 6, 8 are presented which have
some benefits rather than the explicitly constructed QC and APM
LDPC codes in minimum-distance, cycle distributions and biterror-rate performances.
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