272 research outputs found
Design of LDPC Code Ensembles with Fast Convergence Properties
The design of low-density parity-check (LDPC) code ensembles optimized for a
finite number of decoder iterations is investigated. Our approach employs EXIT
chart analysis and differential evolution to design such ensembles for the
binary erasure channel and additive white Gaussian noise channel. The error
rates of codes optimized for various numbers of decoder iterations are compared
and it is seen that in the cases considered, the best performance for a given
number of decoder iterations is achieved by codes which are optimized for this
particular number. The design of generalized LDPC (GLDPC) codes is also
considered, showing that these structures can offer better performance than
LDPC codes for low-iteration-number designs. Finally, it is illustrated that
LDPC codes which are optimized for a small number of iterations exhibit
significant deviations in terms of degree distribution and weight enumerators
with respect to LDPC codes returned by more conventional design tools.Comment: 6 pages, 5 figures, Submitted to the 3rd International Black Sea
Conference on Communications and Networking (IEEE BlackSeaCom 2015
A Fast Convergence Density Evolution Algorithm for Optimal Rate LDPC Codes in BEC
We derive a new fast convergent Density Evolution algorithm for finding
optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure
channel (BEC). The fast convergence property comes from the modified Density
Evolution (DE), a numerical method for analyzing the behavior of iterative
decoding convergence of a LDPC code. We have used the method of [16] for
designing of a LDPC code with optimal rate. This has been done for a given
parity check node degree distribution, erasure probability and specified DE
constraint. The fast behavior of DE and found optimal rate with this method
compare with the previous DE constraint.Comment: This Paper is a draft of final paper which represented in 7th
International Symposium on Telecommunications (IST'2014
Capacity-Achieving Ensembles of Accumulate-Repeat-Accumulate Codes for the Erasure Channel with Bounded Complexity
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes
which asymptotically achieve capacity on the binary erasure channel (BEC) with
{\em bounded complexity}, per information bit, of encoding and decoding. It
also introduces symmetry properties which play a central role in the
construction of capacity-achieving ensembles for the BEC with bounded
complexity. The results here improve on the tradeoff between performance and
complexity provided by previous constructions of capacity-achieving ensembles
of codes defined on graphs. The superiority of ARA codes with moderate to large
block length is exemplified by computer simulations which compare their
performance with those of previously reported capacity-achieving ensembles of
LDPC and IRA codes. The ARA codes also have the advantage of being systematic.Comment: Submitted to IEEE Trans. on Information Theory, December 1st, 2005.
Includes 50 pages and 13 figure
Spatially Coupled LDPC Codes Constructed from Protographs
In this paper, we construct protograph-based spatially coupled low-density
parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or
uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L,
we obtain a flexible family of code ensembles with varying rates and frame
lengths that can share the same encoding and decoding architecture for
arbitrary L. We demonstrate that the resulting codes combine the best features
of optimized irregular and regular codes in one design: capacity approaching
iterative belief propagation (BP) decoding thresholds and linear growth of
minimum distance with block length. In particular, we show that, for
sufficiently large L, the BP thresholds on both the binary erasure channel
(BEC) and the binary-input additive white Gaussian noise channel (AWGNC)
saturate to a particular value significantly better than the BP decoding
threshold and numerically indistinguishable from the optimal maximum
a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all
variable nodes in the coupled chain have degree greater than two,
asymptotically the error probability converges at least doubly exponentially
with decoding iterations and we obtain sequences of asymptotically good LDPC
codes with fast convergence rates and BP thresholds close to the Shannon limit.
Further, the gap to capacity decreases as the density of the graph increases,
opening up a new way to construct capacity achieving codes on memoryless
binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor
On a Low-Rate TLDPC Code Ensemble and the Necessary Condition on the Linear Minimum Distance for Sparse-Graph Codes
This paper addresses the issue of design of low-rate sparse-graph codes with
linear minimum distance in the blocklength. First, we define a necessary
condition which needs to be satisfied when the linear minimum distance is to be
ensured. The condition is formulated in terms of degree-1 and degree-2 variable
nodes and of low-weight codewords of the underlying code, and it generalizies
results known for turbo codes [8] and LDPC codes. Then, we present a new
ensemble of low-rate codes, which itself is a subclass of TLDPC codes [4], [5],
and which is designed under this necessary condition. The asymptotic analysis
of the ensemble shows that its iterative threshold is situated close to the
Shannon limit. In addition to the linear minimum distance property, it has a
simple structure and enjoys a low decoding complexity and a fast convergence.Comment: submitted to IEEE Trans. on Communication
Density Evolution for Asymmetric Memoryless Channels
Density evolution is one of the most powerful analytical tools for
low-density parity-check (LDPC) codes and graph codes with message passing
decoding algorithms. With channel symmetry as one of its fundamental
assumptions, density evolution (DE) has been widely and successfully applied to
different channels, including binary erasure channels, binary symmetric
channels, binary additive white Gaussian noise channels, etc. This paper
generalizes density evolution for non-symmetric memoryless channels, which in
turn broadens the applications to general memoryless channels, e.g. z-channels,
composite white Gaussian noise channels, etc. The central theorem underpinning
this generalization is the convergence to perfect projection for any fixed size
supporting tree. A new iterative formula of the same complexity is then
presented and the necessary theorems for the performance concentration theorems
are developed. Several properties of the new density evolution method are
explored, including stability results for general asymmetric memoryless
channels. Simulations, code optimizations, and possible new applications
suggested by this new density evolution method are also provided. This result
is also used to prove the typicality of linear LDPC codes among the coset code
ensemble when the minimum check node degree is sufficiently large. It is shown
that the convergence to perfect projection is essential to the belief
propagation algorithm even when only symmetric channels are considered. Hence
the proof of the convergence to perfect projection serves also as a completion
of the theory of classical density evolution for symmetric memoryless channels.Comment: To appear in the IEEE Transactions on Information Theor
Spatially Coupled Codes and Optical Fiber Communications: An Ideal Match?
In this paper, we highlight the class of spatially coupled codes and discuss
their applicability to long-haul and submarine optical communication systems.
We first demonstrate how to optimize irregular spatially coupled LDPC codes for
their use in optical communications with limited decoding hardware complexity
and then present simulation results with an FPGA-based decoder where we show
that very low error rates can be achieved and that conventional block-based
LDPC codes can be outperformed. In the second part of the paper, we focus on
the combination of spatially coupled LDPC codes with different demodulators and
detectors, important for future systems with adaptive modulation and for
varying channel characteristics. We demonstrate that SC codes can be employed
as universal, channel-agnostic coding schemes.Comment: Invited paper to be presented in the special session on "Signal
Processing, Coding, and Information Theory for Optical Communications" at
IEEE SPAWC 201
On the Convergence Speed of Spatially Coupled LDPC Ensembles
Spatially coupled low-density parity-check codes show an outstanding
performance under the low-complexity belief propagation (BP) decoding
algorithm. They exhibit a peculiar convergence phenomenon above the BP
threshold of the underlying non-coupled ensemble, with a wave-like convergence
propagating through the spatial dimension of the graph, allowing to approach
the MAP threshold. We focus on this particularly interesting regime in between
the BP and MAP thresholds.
On the binary erasure channel, it has been proved that the information
propagates with a constant speed toward the successful decoding solution. We
derive an upper bound on the propagation speed, only depending on the basic
parameters of the spatially coupled code ensemble such as degree distribution
and the coupling factor . We illustrate the convergence speed of different
code ensembles by simulation results, and show how optimizing degree profiles
helps to speed up the convergence.Comment: 11 pages, 6 figure
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