79 research outputs found
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
Simultaneous Code/Error-Trellis Reduction for Convolutional Codes Using Shifted Code/Error-Subsequences
In this paper, we show that the code-trellis and the error-trellis for a
convolutional code can be reduced simultaneously, if reduction is possible.
Assume that the error-trellis can be reduced using shifted error-subsequences.
In this case, if the identical shifts occur in the subsequences of each code
path, then the code-trellis can also be reduced. First, we obtain pairs of
transformations which generate the identical shifts both in the subsequences of
the code-path and in those of the error-path. Next, by applying these
transformations to the generator matrix and the parity-check matrix, we show
that reduction of these matrices is accomplished simultaneously, if it is
possible. Moreover, it is shown that the two associated trellises are also
reduced simultaneously.Comment: 5 pages, submitted to the 2011 IEEE International Symposium on
Information Theor
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
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
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