291 research outputs found
Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes with Large Girth
We propose a low-complexity method to find quasi-cyclic low-density
parity-check block codes with girth 10 or 12 and shorter length than those
designed through classical approaches. The method is extended to time-invariant
spatially coupled low-density parity-check convolutional codes, permitting to
achieve small syndrome former constraint lengths. Several numerical examples
are given to show its effectiveness.Comment: 4 pages, 3 figures, 1 table, accepted for publication in IEEE
Communications Letter
Low-Density Arrays of Circulant Matrices: Rank and Row-Redundancy Analysis, and Quasi-Cyclic LDPC Codes
This paper is concerned with general analysis on the rank and row-redundancy
of an array of circulants whose null space defines a QC-LDPC code. Based on the
Fourier transform and the properties of conjugacy classes and Hadamard products
of matrices, we derive tight upper bounds on rank and row-redundancy for
general array of circulants, which make it possible to consider row-redundancy
in constructions of QC-LDPC codes to achieve better performance. We further
investigate the rank of two types of construction of QC-LDPC codes:
constructions based on Vandermonde Matrices and Latin Squares and give
combinatorial expression of the exact rank in some specific cases, which
demonstrates the tightness of the bound we derive. Moreover, several types of
new construction of QC-LDPC codes with large row-redundancy are presented and
analyzed.Comment: arXiv admin note: text overlap with arXiv:1004.118
Hierarchical and High-Girth QC LDPC Codes
We present a general approach to designing capacity-approaching high-girth
low-density parity-check (LDPC) codes that are friendly to hardware
implementation. Our methodology starts by defining a new class of
"hierarchical" quasi-cyclic (HQC) LDPC codes that generalizes the structure of
quasi-cyclic (QC) LDPC codes. Whereas the parity check matrices of QC LDPC
codes are composed of circulant sub-matrices, those of HQC LDPC codes are
composed of a hierarchy of circulant sub-matrices that are in turn constructed
from circulant sub-matrices, and so on, through some number of levels. We show
how to map any class of codes defined using a protograph into a family of HQC
LDPC codes. Next, we present a girth-maximizing algorithm that optimizes the
degrees of freedom within the family of codes to yield a high-girth HQC LDPC
code. Finally, we discuss how certain characteristics of a code protograph will
lead to inevitable short cycles, and show that these short cycles can be
eliminated using a "squashing" procedure that results in a high-girth QC LDPC
code, although not a hierarchical one. We illustrate our approach with designed
examples of girth-10 QC LDPC codes obtained from protographs of one-sided
spatially-coupled codes.Comment: Submitted to IEEE Transactions on Information THeor
New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes
This paper presents several new construction techniques for low-density
parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on
specific classes of combinatorial designs, the improved code design focuses on
high-rate structured codes with constant column weights 3 and higher. The
proposed codes are efficiently encodable and exhibit good structural
properties. Experimental results on decoding performance with the sum-product
algorithm show that the novel codes offer substantial practical application
potential, for instance, in high-speed applications in magnetic recording and
optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications
Design and Analysis of Time-Invariant SC-LDPC Convolutional Codes With Small Constraint Length
In this paper, we deal with time-invariant spatially coupled low-density
parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches
usually start from quasi-cyclic low-density parity-check (QC-LDPC) block codes
and exploit suitable unwrapping procedures to obtain SC-LDPC-CCs. We show that
the direct design of the SC-LDPC-CCs syndrome former matrix or, equivalently,
the symbolic parity-check matrix, leads to codes with smaller syndrome former
constraint lengths with respect to the best solutions available in the
literature. We provide theoretical lower bounds on the syndrome former
constraint length for the most relevant families of SC-LDPC-CCs, under
constraints on the minimum length of cycles in their Tanner graphs. We also
propose new code design techniques that approach or achieve such theoretical
limits.Comment: 30 pages, 5 figures, accepted for publication in IEEE Transactions on
Communication
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