261 research outputs found
Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel
In this paper, we show that Quasi-Cyclic LDPC codes can efficiently
accommodate the hybrid iterative/ML decoding over the binary erasure channel.
We demonstrate that the quasi-cyclic structure of the parity-check matrix can
be advantageously used in order to significantly reduce the complexity of the
ML decoding. This is achieved by a simple row/column permutation that
transforms a QC matrix into a pseudo-band form. Based on this approach, we
propose a class of QC-LDPC codes with almost ideal error correction performance
under the ML decoding, while the required number of row/symbol operations
scales as , where is the number of source symbols.Comment: 6 pages, ISITA1
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
Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes
In this paper, a simple, general-purpose and effective tool for the design of
low-density parity-check (LDPC) codes for iterative correction of bursts of
erasures is presented. The design method consists in starting from the
parity-check matrix of an LDPC code and developing an optimized parity-check
matrix, with the same performance on the memory-less erasure channel, and
suitable also for the iterative correction of single bursts of erasures. The
parity-check matrix optimization is performed by an algorithm called pivot
searching and swapping (PSS) algorithm, which executes permutations of
carefully chosen columns of the parity-check matrix, after a local analysis of
particular variable nodes called stopping set pivots. This algorithm can be in
principle applied to any LDPC code. If the input parity-check matrix is
designed for achieving good performance on the memory-less erasure channel,
then the code obtained after the application of the PSS algorithm provides good
joint correction of independent erasures and single erasure bursts. Numerical
results are provided in order to show the effectiveness of the PSS algorithm
when applied to different categories of LDPC codes.Comment: 15 pages, 4 figures. IEEE Trans. on Communications, accepted
(submitted in Feb. 2007
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
Spatially Coupled LDPC Codes for Decode-and-Forward in Erasure Relay Channel
We consider spatially-coupled protograph-based LDPC codes for the three
terminal erasure relay channel. It is observed that BP threshold value, the
maximal erasure probability of the channel for which decoding error probability
converges to zero, of spatially-coupled codes, in particular spatially-coupled
MacKay-Neal code, is close to the theoretical limit for the relay channel.
Empirical results suggest that spatially-coupled protograph-based LDPC codes
have great potential to achieve theoretical limit of a general relay channel.Comment: 7 pages, extended version of ISIT201
Lowering the Error Floor of LDPC Codes Using Cyclic Liftings
Cyclic liftings are proposed to lower the error floor of low-density
parity-check (LDPC) codes. The liftings are designed to eliminate dominant
trapping sets of the base code by removing the short cycles which form the
trapping sets. We derive a necessary and sufficient condition for the cyclic
permutations assigned to the edges of a cycle of length in the
base graph such that the inverse image of in the lifted graph consists of
only cycles of length strictly larger than . The proposed method is
universal in the sense that it can be applied to any LDPC code over any channel
and for any iterative decoding algorithm. It also preserves important
properties of the base code such as degree distributions, encoder and decoder
structure, and in some cases, the code rate. The proposed method is applied to
both structured and random codes over the binary symmetric channel (BSC). The
error floor improves consistently by increasing the lifting degree, and the
results show significant improvements in the error floor compared to the base
code, a random code of the same degree distribution and block length, and a
random lifting of the same degree. Similar improvements are also observed when
the codes designed for the BSC are applied to the additive white Gaussian noise
(AWGN) channel
Link-Layer Coding for GNSS Navigation Messages
In this paper, we face the problem of ensuring reliability of Global Navigation Satellite Systems (GNSSs) in harsh channel conditions, where obstacles and scatter cause long outage events that cannot be counteracted with channel coding only. Our novel approach, stemming from information-theoretic considerations, is based on link-layer coding (LLC). LLC allows us to significantly improve the efficiency in terms of time-to-first-fix with respect to current operational GNSSs, which adopt carousel transmission. First, we investigate the maximum theoretical LLC gain under different Land Mobile Satellite channel conditions. Then, some practical LLC coding schemes, namely, fountain codes and a novel low-density parity-check plus low-rate repetition coding, are proposed and tested in realistic single-satellite and multi-satellite Land Mobile Satellite scenarios, considering the Galileo I/NAV message as study case. Simulation results show that our designed schemes largely improve on carousel transmission and achieve near-optimal performance with limited increase in complexity. Also, back-compatibility of LLC is assessed with respect to present-time GNSS specifications. © 2018 Institute of Navigation
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