92 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
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
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
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
Characterization and Efficient Search of Non-Elementary Trapping Sets of LDPC Codes with Applications to Stopping Sets
In this paper, we propose a characterization for non-elementary trapping sets
(NETSs) of low-density parity-check (LDPC) codes. The characterization is based
on viewing a NETS as a hierarchy of embedded graphs starting from an ETS. The
characterization corresponds to an efficient search algorithm that under
certain conditions is exhaustive. As an application of the proposed
characterization/search, we obtain lower and upper bounds on the stopping
distance of LDPC codes.
We examine a large number of regular and irregular LDPC codes, and
demonstrate the efficiency and versatility of our technique in finding lower
and upper bounds on, and in many cases the exact value of, . Finding
, or establishing search-based lower or upper bounds, for many of the
examined codes are out of the reach of any existing algorithm
- …