37 research outputs found
A Variational Inference Framework for Soft-In-Soft-Out Detection in Multiple Access Channels
We propose a unified framework for deriving and studying soft-in-soft-out
(SISO) detection in interference channels using the concept of variational
inference. The proposed framework may be used in multiple-access interference
(MAI), inter-symbol interference (ISI), and multiple-input multiple-outpu
(MIMO) channels. Without loss of generality, we will focus our attention on
turbo multiuser detection, to facilitate a more concrete discussion. It is
shown that, with some loss of optimality, variational inference avoids the
exponential complexity of a posteriori probability (APP) detection by
optimizing a closely-related, but much more manageable, objective function
called variational free energy. In addition to its systematic appeal, there are
several other advantages to this viewpoint. First of all, it provides unified
and rigorous justifications for numerous detectors that were proposed on
radically different grounds, and facilitates convenient joint detection and
decoding (utilizing the turbo principle) when error-control codes are
incorporated. Secondly, efficient joint parameter estimation and data detection
is possible via the variational expectation maximization (EM) algorithm, such
that the detrimental effect of inaccurate channel knowledge at the receiver may
be dealt with systematically. We are also able to extend BPSK-based SISO
detection schemes to arbitrary square QAM constellations in a rigorous manner
using a variational argument.Comment: Submitted to Transactions on Information Theor
Optimality and duality of the turbo decoder
Proceedings of the IEEE, 95(6): pp. 1362-1377.The near-optimal performance of the turbo
decoder has been a source of intrigue among communications
engineers and information theorists, given its ad hoc origins
that were seemingly disconnected from optimization theory.
Naturally one would inquire whether the favorable performance
might be explained by characterizing the turbo decoder
via some optimization criterion or performance index. Recently,
two such characterizations have surfaced. One draws from
statistical mechanics and aims to minimize the Bethe approximation
to a free energy measure. The other characterization
involves constrained likelihood estimation, a setting perhaps
more familiar to communications engineers. The intent of
this paper is to assemble a tutorial overview of these recent
developments, and more importantly to identify the formal
mathematical duality between the two viewpoints. The paper
includes tutorial background material on the information
geometry tools used in analyzing the turbo decoder, and the
analysis accommodates both the parallel concatenation and
serial concatenation schemes in a common framework
Joint Equalization and Decoding via Convex Optimization
The unifying theme of this dissertation is the development of new solutions for decoding and inference problems based on convex optimization methods. Th first part considers the joint detection and decoding problem for low-density parity-check (LDPC) codes on finite-state channels (FSCs). Hard-disk drives (or magnetic recording systems), where the required error rate (after decoding) is too low to be verifiable by simulation, are most important applications of this research.
Recently, LDPC codes have attracted a lot of attention in the magnetic storage industry and some hard-disk drives have started using iterative decoding. Despite progress in the area of reduced-complexity detection and decoding algorithms, there has been some resistance to the deployment of turbo-equalization (TE) structures (with iterative detectors/decoders) in magnetic-recording systems because of error floors and the difficulty of accurately predicting performance at very low error rates.
To address this problem for channels with memory, such as FSCs, we propose a new decoding algorithms based on a well-defined convex optimization problem. In particular, it is based on the linear-programing (LP) formulation of the joint decoding problem for LDPC codes over FSCs. It exhibits two favorable properties: provable convergence and predictable error-floors (via pseudo-codeword analysis).
Since general-purpose LP solvers are too complex to make the joint LP decoder feasible for practical purposes, we develop an efficient iterative solver for the joint LP
decoder by taking advantage of its dual-domain structure. The main advantage of this approach is that it combines the predictability and superior performance of joint LP decoding with the computational complexity of TE.
The second part of this dissertation considers the matrix completion problem for the recovery of a data matrix from incomplete, or even corrupted entries of an unknown matrix. Recommender systems are good representatives of this problem, and this research is important for the design of information retrieval systems which require very high scalability. We show that our IMP algorithm reduces the well-known cold-start problem associated with collaborative filtering systems in practice
An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation
In this work we design a receiver that iteratively passes soft information
between the channel estimation and data decoding stages. The receiver
incorporates sparsity-based parametric channel estimation. State-of-the-art
sparsity-based iterative receivers simplify the channel estimation problem by
restricting the multipath delays to a grid. Our receiver does not impose such a
restriction. As a result it does not suffer from the leakage effect, which
destroys sparsity. Communication at near capacity rates in high SNR requires a
large modulation order. Due to the close proximity of modulation symbols in
such systems, the grid-based approximation is of insufficient accuracy. We show
numerically that a state-of-the-art iterative receiver with grid-based sparse
channel estimation exhibits a bit-error-rate floor in the high SNR regime. On
the contrary, our receiver performs very close to the perfect channel state
information bound for all SNR values. We also demonstrate both theoretically
and numerically that parametric channel estimation works well in dense
channels, i.e., when the number of multipath components is large and each
individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin
A Novel Conflict-Free Memory and Processor Architecture for DVB-T2 LDPC Decoding
In this paper, we present a flexible architecture for an LDPC decoder that fully exploits the structure of the codes defined in the DVB-T2 standard (Digital Video Broadcasting - Second Generation Terrestrial). We propose a processor and memory architecture which uses the flooding schedule and has no memory access conflicts, which are encountered in serial schedule decoders proposed in the literature. Thus, unlike previous works, we do not require any extra logic or ad hoc designs to resolve memory conflicts. Despite the typically slower convergence of flooding schedule compared to serial schedule decoders, our ar- chitecture meets the throughput and BER requirements specified in the DVB-T2 standard. Our design allows a trade-off between memory size and performance by the selection of the number of bits per message without affecting the general memory arrangement. Besides, our architecture is not algorithm specific: any check-node message processing algorithm can be used (Sum-Product, Min-Sum, etc.) without modifying the basic architecture. Furthermore, by simply adding relevant small ROM tables, we get a decoder that is fully compatible with all three second generation DVB standards (DVB-T2, DVB-S2 and DVB-C2). We present simulation results to demonstrate the viability of our solution both functionally and in terms of the bit-error rate performance. We also discuss the memory requirements and the throughput of the architecture, and present preliminary synthesis results in CMOS 130nm technology
High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
We consider the problem of high-dimensional Gaussian graphical model
selection. We identify a set of graphs for which an efficient estimation
algorithm exists, and this algorithm is based on thresholding of empirical
conditional covariances. Under a set of transparent conditions, we establish
structural consistency (or sparsistency) for the proposed algorithm, when the
number of samples n=omega(J_{min}^{-2} log p), where p is the number of
variables and J_{min} is the minimum (absolute) edge potential of the graphical
model. The sufficient conditions for sparsistency are based on the notion of
walk-summability of the model and the presence of sparse local vertex
separators in the underlying graph. We also derive novel non-asymptotic
necessary conditions on the number of samples required for sparsistency
Méthodes de codage et d'estimation adaptative appliquées aux communications sans fil
Les recherches et les contributions présentées portent sur des techniques de traitement du signal appliquées aux communications sans fil. Elles s’articulent autour des points suivants : (1) l’estimation adaptative de canaux de communication dans différents contextes applicatifs, (2) la correction de bruit impulsionnel et la réduction du niveau de PAPR (Peak to Average Power Ratio) dans un système multi-porteuse, (3) l’optimisation de schémas de transmission pour la diffusion sur des canaux gaussiens avec/sans contrainte de sécurité, (4) l’analyse, l’interprétation et l’amélioration des algorithmes de décodage itératif par le biais de l’optimisation, de la théorie des jeux et des outils statistiques. L’accent est plus particulièrement mis sur le dernier thème
Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance
We examine LDPC codes decoded using linear programming (LP). Four
contributions to the LP framework are presented. First, a new method of
tightening the LP relaxation, and thus improving the LP decoder, is proposed.
Second, we present an algorithm which calculates a lower bound on the minimum
distance of a specific code. This algorithm exhibits complexity which scales
quadratically with the block length. Third, we propose a method to obtain a
tight lower bound on the fractional distance, also with quadratic complexity,
and thus less than previously-existing methods. Finally, we show how the
fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can
be obtained.Comment: 17 pages, 8 figures, Submitted to IEEE Transactions on Information
Theor