186 research outputs found
Terminated LDPC Convolutional Codes with Thresholds Close to Capacity
An ensemble of LDPC convolutional codes with parity-check matrices composed
of permutation matrices is considered. The convergence of the iterative belief
propagation based decoder for terminated convolutional codes in the ensemble is
analyzed for binary-input output-symmetric memoryless channels using density
evolution techniques. We observe that the structured irregularity in the Tanner
graph of the codes leads to significantly better thresholds when compared to
corresponding LDPC block codes.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
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
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
Windowed Decoding of Protograph-based LDPC Convolutional Codes over Erasure Channels
We consider a windowed decoding scheme for LDPC convolutional codes that is
based on the belief-propagation (BP) algorithm. We discuss the advantages of
this decoding scheme and identify certain characteristics of LDPC convolutional
code ensembles that exhibit good performance with the windowed decoder. We will
consider the performance of these ensembles and codes over erasure channels
with and without memory. We show that the structure of LDPC convolutional code
ensembles is suitable to obtain performance close to the theoretical limits
over the memoryless erasure channel, both for the BP decoder and windowed
decoding. However, the same structure imposes limitations on the performance
over erasure channels with memory.Comment: 18 pages, 9 figures, accepted for publication in the IEEE
Transactions on Information Theor
On the Minimum Distance of Generalized Spatially Coupled LDPC Codes
Families of generalized spatially-coupled low-density parity-check (GSC-LDPC)
code ensembles can be formed by terminating protograph-based generalized LDPC
convolutional (GLDPCC) codes. It has previously been shown that ensembles of
GSC-LDPC codes constructed from a protograph have better iterative decoding
thresholds than their block code counterparts, and that, for large termination
lengths, their thresholds coincide with the maximum a-posteriori (MAP) decoding
threshold of the underlying generalized LDPC block code ensemble. Here we show
that, in addition to their excellent iterative decoding thresholds, ensembles
of GSC-LDPC codes are asymptotically good and have large minimum distance
growth rates.Comment: Submitted to the IEEE International Symposium on Information Theory
201
Design and Performance of Rate-compatible Non-Binary LDPC Convolutional Codes
In this paper, we present a construction method of non-binary low-density
parity-check (LDPC) convolutional codes. Our construction method is an
extension of Felstroem and Zigangirov construction for non-binary LDPC
convolutional codes. The rate-compatibility of the non-binary convolutional
code is also discussed. The proposed rate-compatible code is designed from one
single mother (2,4)-regular non-binary LDPC convolutional code of rate 1/2.
Higher-rate codes are produced by puncturing the mother code and lower-rate
codes are produced by multiplicatively repeating the mother code. Simulation
results show that non-binary LDPC convolutional codes of rate 1/2 outperform
state-of-the-art binary LDPC convolutional codes with comparable constraint bit
length. Also the derived low-rate and high-rate non-binary LDPC convolutional
codes exhibit good decoding performance without loss of large gap to the
Shannon limits.Comment: 8 pages, submitted to IEICE transactio
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
Threshold Analysis of Non-Binary Spatially-Coupled LDPC Codes with Windowed Decoding
In this paper we study the iterative decoding threshold performance of
non-binary spatially-coupled low-density parity-check (NB-SC-LDPC) code
ensembles for both the binary erasure channel (BEC) and the binary-input
additive white Gaussian noise channel (BIAWGNC), with particular emphasis on
windowed decoding (WD). We consider both (2,4)-regular and (3,6)-regular
NB-SC-LDPC code ensembles constructed using protographs and compute their
thresholds using protograph versions of NB density evolution and NB extrinsic
information transfer analysis. For these code ensembles, we show that WD of
NB-SC-LDPC codes, which provides a significant decrease in latency and
complexity compared to decoding across the entire parity-check matrix, results
in a negligible decrease in the near-capacity performance for a sufficiently
large window size W on both the BEC and the BIAWGNC. Also, we show that
NB-SC-LDPC code ensembles exhibit gains in the WD threshold compared to the
corresponding block code ensembles decoded across the entire parity-check
matrix, and that the gains increase as the finite field size q increases.
Moreover, from the viewpoint of decoding complexity, we see that (3,6)-regular
NB-SC-LDPC codes are particularly attractive due to the fact that they achieve
near-capacity thresholds even for small q and W.Comment: 6 pages, 8 figures; submitted to 2014 IEEE International Symposium on
Information Theor
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
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