750 research outputs found
Interior Point Decoding for Linear Vector Channels
In this paper, a novel decoding algorithm for low-density parity-check (LDPC)
codes based on convex optimization is presented. The decoding algorithm, called
interior point decoding, is designed for linear vector channels. The linear
vector channels include many practically important channels such as inter
symbol interference channels and partial response channels. It is shown that
the maximum likelihood decoding (MLD) rule for a linear vector channel can be
relaxed to a convex optimization problem, which is called a relaxed MLD
problem. The proposed decoding algorithm is based on a numerical optimization
technique so called interior point method with barrier function. Approximate
variations of the gradient descent and the Newton methods are used to solve the
convex optimization problem. In a decoding process of the proposed algorithm, a
search point always lies in the fundamental polytope defined based on a
low-density parity-check matrix. Compared with a convectional joint message
passing decoder, the proposed decoding algorithm achieves better BER
performance with less complexity in the case of partial response channels in
many cases.Comment: 18 pages, 17 figures, The paper has been submitted to IEEE
Transaction on Information Theor
Graph-Based Decoding in the Presence of ISI
We propose an approximation of maximum-likelihood detection in ISI channels
based on linear programming or message passing. We convert the detection
problem into a binary decoding problem, which can be easily combined with LDPC
decoding. We show that, for a certain class of channels and in the absence of
coding, the proposed technique provides the exact ML solution without an
exponential complexity in the size of channel memory, while for some other
channels, this method has a non-diminishing probability of failure as SNR
increases. Some analysis is provided for the error events of the proposed
technique under linear programming.Comment: 25 pages, 8 figures, Submitted to IEEE Transactions on Information
Theor
An Iterative Joint Linear-Programming Decoding of LDPC Codes and Finite-State Channels
In this paper, we introduce an efficient iterative solver for the joint
linear-programming (LP) decoding of low-density parity-check (LDPC) codes and
finite-state channels (FSCs). In particular, we extend the approach of
iterative approximate LP decoding, proposed by Vontobel and Koetter and
explored by Burshtein, to this problem. By taking advantage of the dual-domain
structure of the joint decoding LP, we obtain a convergent iterative algorithm
for joint LP decoding whose structure is similar to BCJR-based turbo
equalization (TE). The result is a joint iterative decoder whose complexity is
similar to TE but whose performance is similar to joint LP decoding. The main
advantage of this decoder is that it appears to provide the predictability of
joint LP decoding and superior performance with the computational complexity of
TE.Comment: To appear in Proc. IEEE ICC 2011, Kyoto, Japan, June 5-9, 201
An Iteratively Decodable Tensor Product Code with Application to Data Storage
The error pattern correcting code (EPCC) can be constructed to provide a
syndrome decoding table targeting the dominant error events of an inter-symbol
interference channel at the output of the Viterbi detector. For the size of the
syndrome table to be manageable and the list of possible error events to be
reasonable in size, the codeword length of EPCC needs to be short enough.
However, the rate of such a short length code will be too low for hard drive
applications. To accommodate the required large redundancy, it is possible to
record only a highly compressed function of the parity bits of EPCC's tensor
product with a symbol correcting code. In this paper, we show that the proposed
tensor error-pattern correcting code (T-EPCC) is linear time encodable and also
devise a low-complexity soft iterative decoding algorithm for EPCC's tensor
product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that
T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a
1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB
T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same
decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor
Product Code with Application to Data Storage
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
Asymptotic Analysis and Design of Iterative Receivers for Non Linear ISI Channels
International audienceIn this paper, iterative receiver analysis and design for non linear satellite channels is investigated. To do so, an EXtrinsic Information Transfer (EXIT) chart-based optimization is applied using two major assumptions: the equalizer outputs follow a Gaussian Mixture distribution since we use non-binary modulations and partial interleavers are used between the Low Density Parity Check (LDPC) code and the mapper. Achievable rates, performance and thresholds of the optimized receiver are analysed. The objective in fine is to answer the question: Is it worth optimizing an iterative receiver for non linear satellite channels
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