4,767 research outputs found
Approximate Message Passing under Finite Alphabet Constraints
In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which
the sparse original signal is drawn from a finite alphabet. To solve this
problem we propose an iterative message passing algorithm, which capitalises
not only on the sparsity but by means of a prior distribution also on the
discrete nature of the original signal. In our numerical experiments we test
this algorithm in combination with a Rademacher measurement matrix and a
measurement matrix derived from the random demodulator, which enables
compressive sampling of analogue signals. Our results show in both cases
significant performance gains over a linear programming based approach to the
considered BPDN problem. We also compare the proposed algorithm to a similar
message passing based algorithm without prior knowledge and observe an even
larger performance improvement.Comment: 4 pages, 2 figures, to appear in IEEE International Conference on
Acoustics, Speech, and Signal Processing ICASSP 201
Generalized Approximate Message-Passing Decoder for Universal Sparse Superposition Codes
Sparse superposition (SS) codes were originally proposed as a
capacity-achieving communication scheme over the additive white Gaussian noise
channel (AWGNC) [1]. Very recently, it was discovered that these codes are
universal, in the sense that they achieve capacity over any memoryless channel
under generalized approximate message-passing (GAMP) decoding [2], although
this decoder has never been stated for SS codes. In this contribution we
introduce the GAMP decoder for SS codes, we confirm empirically the
universality of this communication scheme through its study on various channels
and we provide the main analysis tools: state evolution and potential. We also
compare the performance of GAMP with the Bayes-optimal MMSE decoder. We
empirically illustrate that despite the presence of a phase transition
preventing GAMP to reach the optimal performance, spatial coupling allows to
boost the performance that eventually tends to capacity in a proper limit. We
also prove that, in contrast with the AWGNC case, SS codes for binary input
channels have a vanishing error floor in the limit of large codewords.
Moreover, the performance of Hadamard-based encoders is assessed for practical
implementations
Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View
These are the notes for a set of lectures delivered by the two authors at the
Les Houches Summer School on `Complex Systems' in July 2006. They provide an
introduction to the basic concepts in modern (probabilistic) coding theory,
highlighting connections with statistical mechanics. We also stress common
concepts with other disciplines dealing with similar problems that can be
generically referred to as `large graphical models'.
While most of the lectures are devoted to the classical channel coding
problem over simple memoryless channels, we present a discussion of more
complex channel models. We conclude with an overview of the main open
challenges in the field.Comment: Lectures at Les Houches Summer School on `Complex Systems', July
2006, 44 pages, 25 ps figure
Message-Passing Algorithms for Channel Estimation and Decoding Using Approximate Inference
We design iterative receiver schemes for a generic wireless communication
system by treating channel estimation and information decoding as an inference
problem in graphical models. We introduce a recently proposed inference
framework that combines belief propagation (BP) and the mean field (MF)
approximation and includes these algorithms as special cases. We also show that
the expectation propagation and expectation maximization algorithms can be
embedded in the BP-MF framework with slight modifications. By applying the
considered inference algorithms to our probabilistic model, we derive four
different message-passing receiver schemes. Our numerical evaluation
demonstrates that the receiver based on the BP-MF framework and its variant
based on BP-EM yield the best compromise between performance, computational
complexity and numerical stability among all candidate algorithms.Comment: Accepted for publication in the Proceedings of 2012 IEEE
International Symposium on Information Theor
- …