1,772 research outputs found
Deriving Good LDPC Convolutional Codes from LDPC Block Codes
Low-density parity-check (LDPC) convolutional codes are capable of achieving
excellent performance with low encoding and decoding complexity. In this paper
we discuss several graph-cover-based methods for deriving families of
time-invariant and time-varying LDPC convolutional codes from LDPC block codes
and show how earlier proposed LDPC convolutional code constructions can be
presented within this framework. Some of the constructed convolutional codes
significantly outperform the underlying LDPC block codes. We investigate some
possible reasons for this "convolutional gain," and we also discuss the ---
mostly moderate --- decoder cost increase that is incurred by going from LDPC
block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010;
revised August 2010, revised November 2010 (essentially final version).
(Besides many small changes, the first and second revised versions contain
corrected entries in Tables I and II.
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
Extended Non-Binary Low-Density Parity-Check Codes over Erasure Channels
Based on the extended binary image of non-binary LDPC codes, we propose a
method for generating extra redundant bits, such as to decreases the coding
rate of a mother code. The proposed method allows for using the same decoder,
regardless of how many extra redundant bits have been produced, which
considerably increases the flexibility of the system without significantly
increasing its complexity. Extended codes are also optimized for the binary
erasure channel, by using density evolution methods. Nevertheless, the results
presented in this paper can easily be extrapolated to more general channel
models.Comment: ISIT 2011, submitte
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
Optimized puncturing distributions for irregular non-binary LDPC codes
In this paper we design non-uniform bit-wise puncturing distributions for
irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are
optimized by minimizing the decoding threshold of the punctured LDPC code, the
threshold being computed with a Monte-Carlo implementation of Density
Evolution. First, we show that Density Evolution computed with Monte-Carlo
simulations provides accurate (very close) and precise (small variance)
estimates of NB-LDPC code ensemble thresholds. Based on the proposed method, we
analyze several puncturing distributions for regular and semi-regular codes,
obtained either by clustering punctured bits, or spreading them over the
symbol-nodes of the Tanner graph. Finally, optimized puncturing distributions
for non-binary LDPC codes with small maximum degree are presented, which
exhibit a gap between 0.2 and 0.5 dB to the channel capacity, for punctured
rates varying from 0.5 to 0.9.Comment: 6 pages, ISITA1
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