17 research outputs found
Lossy source coding using belief propagation and soft-decimation over LDGM codes
This paper focus on the lossy compression of a binary symmetric source. We propose a new algorithm for binary quantization over low density generator matrix (LDGM) codes. The proposed algorithm is a modified version of the belief propagation (BP) algorithm used in the channel coding framework and has linear complexity in the code block length. We also provide a common framework under which the proposed algorithm and some previously proposed algorithms fit. Simulation results show that our scheme achieves close to state-of-the-art performance with reduced complexity
Lossy Source Coding via Spatially Coupled LDGM Ensembles
We study a new encoding scheme for lossy source compression based on
spatially coupled low-density generator-matrix codes. We develop a
belief-propagation guided-decimation algorithm, and show that this algorithm
allows to approach the optimal distortion of spatially coupled ensembles.
Moreover, using the survey propagation formalism, we also observe that the
optimal distortions of the spatially coupled and individual code ensembles are
the same. Since regular low-density generator-matrix codes are known to achieve
the Shannon rate-distortion bound under optimal encoding as the degrees grow,
our results suggest that spatial coupling can be used to reach the
rate-distortion bound, under a {\it low complexity} belief-propagation
guided-decimation algorithm.
This problem is analogous to the MAX-XORSAT problem in computer science.Comment: Submitted to ISIT 201
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
We investigate an encoding scheme for lossy compression of a binary symmetric
source based on simple spatially coupled Low-Density Generator-Matrix codes.
The degree of the check nodes is regular and the one of code-bits is Poisson
distributed with an average depending on the compression rate. The performance
of a low complexity Belief Propagation Guided Decimation algorithm is
excellent. The algorithmic rate-distortion curve approaches the optimal curve
of the ensemble as the width of the coupling window grows. Moreover, as the
check degree grows both curves approach the ultimate Shannon rate-distortion
limit. The Belief Propagation Guided Decimation encoder is based on the
posterior measure of a binary symmetric test-channel. This measure can be
interpreted as a random Gibbs measure at a "temperature" directly related to
the "noise level of the test-channel". We investigate the links between the
algorithmic performance of the Belief Propagation Guided Decimation encoder and
the phase diagram of this Gibbs measure. The phase diagram is investigated
thanks to the cavity method of spin glass theory which predicts a number of
phase transition thresholds. In particular the dynamical and condensation
"phase transition temperatures" (equivalently test-channel noise thresholds)
are computed. We observe that: (i) the dynamical temperature of the spatially
coupled construction saturates towards the condensation temperature; (ii) for
large degrees the condensation temperature approaches the temperature (i.e.
noise level) related to the information theoretic Shannon test-channel noise
parameter of rate-distortion theory. This provides heuristic insight into the
excellent performance of the Belief Propagation Guided Decimation algorithm.
The paper contains an introduction to the cavity method
Efficient data compression from statistical physics of codes over finite fields
In this paper we discuss a novel data compression technique for binary
symmetric sources based on the cavity method over a Galois Field of order q
(GF(q)). We present a scheme of low complexity and near optimal empirical
performance. The compression step is based on a reduction of sparse low density
parity check codes over GF(q) and is done through the so called reinforced
belief-propagation equations. These reduced codes appear to have a non-trivial
geometrical modification of the space of codewords which makes such compression
computationally feasible. The computational complexity is O(d.n.q.log(q)) per
iteration, where d is the average degree of the check nodes and n is the number
of bits. For our code ensemble, decompression can be done in a time linear in
the code's length by a simple leaf-removal algorithm.Comment: 10 pages, 4 figure
Cancelamento de interferência em sistemas celulares distribuídos
Doutoramento em Engenharia ElectrotécnicaO tema principal desta tese é o problema de cancelamento de interferência
para sistemas multi-utilizador, com antenas distribuídas. Como tal, ao iniciar,
uma visão geral das principais propriedades de um sistema de antenas
distribuídas é apresentada. Esta descrição inclui o estudo analítico do impacto
da ligação, dos utilizadores do sistema, a mais antenas distribuídas.
Durante essa análise é demonstrado que a propriedade mais importante do
sistema para obtenção do ganho máximo, através da ligação de mais antenas
de transmissão, é a simetria espacial e que os utilizadores nas fronteiras das
células são os mais bene ciados. Tais resultados são comprovados através
de simulação. O problema de cancelamento de interferência multi-utilizador
é considerado tanto para o caso unidimensional (i.e. sem codi cação) como
para o multidimensional (i.e. com codi cação). Para o caso unidimensional
um algoritmo de pré-codi cação não-linear é proposto e avaliado, tendo
como objectivo a minimização da taxa de erro de bit. Tanto o caso de
portadora única como o de multipla-portadora são abordados, bem como o
cenário de antenas colocadas e distribuidas. É demonstrado que o esquema
proposto pode ser visto como uma extensão do bem conhecido esquema
de zeros forçados, cuja desempenho é provado ser um limite inferior para
o esquema generalizado. O algoritmo é avaliado, para diferentes cenários,
através de simulação, a qual indica desempenho perto do óptimo, com baixa
complexidade. Para o caso multi-dimensional um esquema para efectuar
"dirty paper coding" binário, tendo como base códigos de dupla camada é
proposto. No desenvolvimento deste esquema, a compressão com perdas de
informação, é considerada como um subproblema. Resultados de simulação
indicam transmissão dedigna proxima do limite de Shannon.This thesis focus on the interference cancellation problem for multiuser distributed
antenna systems. As such it starts by giving an overview of the
main properties of a distributed antenna system. This overview includes, an
analytical investigation of the impact of the connection of additional distributed
antennas, to the system users. That analysis shows that the most
important system property to reach the maximum gain, with the connection
of additional transmit antennas, is spatial symmetry and that the users at
the cell borders are the most bene ted. The multiuser interference problem
has been considered for both the one dimensional (i.e. without coding) and
multidimensional (i.e. with coding) cases. In the unidimensional case, we
propose and evaluate a nonlinear precoding algorithm for the minimization
of the bit-error-rate, of a multiuser MIMO system. Both the single-carrier
and multi-carrier cases are tackled as well as the co-located and distributed
scenarios. It is demonstrated that the proposed scheme can be viewed as an
extension of the well-known zero-forcing, whose performance is proven to be
a lower bound for the generalized scheme. The algorithm was validated extensively
through numerical simulations, which indicate a performance close
to the optimal, with reduced complexity. For the multi-dimensional case, a
binary dirty paper coding scheme, base on bilayer codes, is proposed. In the
development of this scheme, we consider the lossy compression of a binary
source as a sub-problem. Simulation results indicate reliable transmission
close to the Shannon limit
Polar Codes are Optimal for Lossy Source Coding
We consider lossy source compression of a binary symmetric source using polar
codes and the low-complexity successive encoding algorithm. It was recently
shown by Arikan that polar codes achieve the capacity of arbitrary symmetric
binary-input discrete memoryless channels under a successive decoding strategy.
We show the equivalent result for lossy source compression, i.e., we show that
this combination achieves the rate-distortion bound for a binary symmetric
source. We further show the optimality of polar codes for various problems
including the binary Wyner-Ziv and the binary Gelfand-Pinsker problemComment: 15 pages, submitted to Transactions on Information Theor