30 research outputs found
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
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
Efficient LDPC Codes over GF(q) for Lossy Data Compression
In this paper we consider the lossy compression of a binary symmetric source.
We present a scheme that provides a low complexity lossy compressor with near
optimal empirical performance. The proposed scheme is based on b-reduced
ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced
Belief Propagation algorithm, a variant of Belief Propagation. The
computational complexity at the encoder is O(.n.q.log q), where is the
average degree of the check nodes. For our code ensemble, decoding can be
performed iteratively following the inverse steps of the leaf removal
algorithm. For a sparse parity-check matrix the number of needed operations is
O(n).Comment: 5 pages, 3 figure
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