585 research outputs found
Deriving Good LDPC Convolutional Codes from LDPC Block Codes
Low-density parity-check (LDPC) convolutional codes are capable of achieving
excellent performance with low encoding and decoding complexity. In this paper
we discuss several graph-cover-based methods for deriving families of
time-invariant and time-varying LDPC convolutional codes from LDPC block codes
and show how earlier proposed LDPC convolutional code constructions can be
presented within this framework. Some of the constructed convolutional codes
significantly outperform the underlying LDPC block codes. We investigate some
possible reasons for this "convolutional gain," and we also discuss the ---
mostly moderate --- decoder cost increase that is incurred by going from LDPC
block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010;
revised August 2010, revised November 2010 (essentially final version).
(Besides many small changes, the first and second revised versions contain
corrected entries in Tables I and II.
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
Progressive Differences Convolutional Low-Density Parity-Check Codes
We present a new family of low-density parity-check (LDPC) convolutional
codes that can be designed using ordered sets of progressive differences. We
study their properties and define a subset of codes in this class that have
some desirable features, such as fixed minimum distance and Tanner graphs
without short cycles. The design approach we propose ensures that these
properties are guaranteed independently of the code rate. This makes these
codes of interest in many practical applications, particularly when high rate
codes are needed for saving bandwidth. We provide some examples of coded
transmission schemes exploiting this new class of codes.Comment: 8 pages, 2 figures. Accepted for publication in IEEE Communications
Letters. Copyright transferred to IEE
Array Convolutional Low-Density Parity-Check Codes
This paper presents a design technique for obtaining regular time-invariant
low-density parity-check convolutional (RTI-LDPCC) codes with low complexity
and good performance. We start from previous approaches which unwrap a
low-density parity-check (LDPC) block code into an RTI-LDPCC code, and we
obtain a new method to design RTI-LDPCC codes with better performance and
shorter constraint length. Differently from previous techniques, we start the
design from an array LDPC block code. We show that, for codes with high rate, a
performance gain and a reduction in the constraint length are achieved with
respect to previous proposals. Additionally, an increase in the minimum
distance is observed.Comment: 4 pages, 2 figures, accepted for publication in IEEE Communications
Letter
Time-Invariant Spatially Coupled Low-Density Parity-Check Codes with Small Constraint Length
We consider a special family of SC-LDPC codes, that is, time-invariant LDPCC
codes, which are known in the literature for a long time. Codes of this kind
are usually designed by starting from QC block codes, and applying suitable
unwrapping procedures. We show that, by directly designing the LDPCC code
syndrome former matrix without the constraints of the underlying QC block code,
it is possible to achieve smaller constraint lengths with respect to the best
solutions available in the literature. We also find theoretical lower bounds on
the syndrome former constraint length for codes with a specified minimum length
of the local cycles in their Tanner graphs. For this purpose, we exploit a new
approach based on a numerical representation of the syndrome former matrix,
which generalizes over a technique we already used to study a special subclass
of the codes here considered.Comment: 5 pages, 4 figures, to be presented at IEEE BlackSeaCom 201
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
Quasi-Cyclic Asymptotically Regular LDPC Codes
Families of "asymptotically regular" LDPC block code ensembles can be formed
by terminating (J,K)-regular protograph-based LDPC convolutional codes. By
varying the termination length, we obtain a large selection of LDPC block code
ensembles with varying code rates, minimum distance that grows linearly with
block length, and capacity approaching iterative decoding thresholds, despite
the fact that the terminated ensembles are almost regular. In this paper, we
investigate the properties of the quasi-cyclic (QC) members of such an
ensemble. We show that an upper bound on the minimum Hamming distance of
members of the QC sub-ensemble can be improved by careful choice of the
component protographs used in the code construction. Further, we show that the
upper bound on the minimum distance can be improved by using arrays of
circulants in a graph cover of the protograph.Comment: To be presented at the 2010 IEEE Information Theory Workshop, Dublin,
Irelan
Compact QC-LDPC Block and SC-LDPC Convolutional Codes for Low-Latency Communications
Low decoding latency and complexity are two important requirements of channel
codes used in many applications, like machine-to-machine communications. In
this paper, we show how these requirements can be fulfilled by using some
special quasi-cyclic low-density parity-check block codes and spatially coupled
low-density parity-check convolutional codes that we denote as compact. They
are defined by parity-check matrices designed according to a recent approach
based on sequentially multiplied columns. This method allows obtaining codes
with girth up to 12. Many numerical examples of practical codes are provided.Comment: 5 pages, 1 figure, presented at IEEE PIMRC 201
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