Weighted universal bit allocation: optimal multiple quantization matrix coding

We introduce a two-stage bit allocation algorithm analogous to the algorithm for weighted universal vector quantization (WUVQ). The encoder uses a collection of possible bit allocations (typically in the form of a collection of quantization matrices) rather than a single bit allocation (or single quantization matrix). We describe both an encoding algorithm for achieving optimal compression using a collection of bit allocations and a technique for designing locally optimal collections of bit allocations. We demonstrate performance on a JPEG style coder using the mean squared error (MSE) distortion measure. On a sequence of medical brain scans, the algorithm achieves up to 2.5 dB improvement over a single bit allocation system, up to 5 dB improvement over a WUVQ with first- and second-stage vector dimensions equal to 16 and 4 respectively, and up to 12 dB improvement over an entropy constrained vector quantizer (ECVQ) using 4 dimensional vectors

Variable dimension weighted universal vector quantization and noiseless coding

A new algorithm for variable dimension weighted universal coding is introduced. Combining the multi-codebook system of weighted universal vector quantization (WUVQ), the partitioning technique of variable dimension vector quantization, and the optimal design strategy common to both, variable dimension WUVQ allows mixture sources to be effectively carved into their component subsources, each of which can then be encoded with the codebook best matched to that source. Application of variable dimension WUVQ to a sequence of medical images provides up to 4.8 dB improvement in signal to quantization noise ratio over WUVQ and up to 11 dB improvement over a standard full-search vector quantizer followed by an entropy code. The optimal partitioning technique can likewise be applied with a collection of noiseless codes, as found in weighted universal noiseless coding (WUNC). The resulting algorithm for variable dimension WUNC is also described

Universal quantization of parametric sources has redundancy k/2 (log n)/n

Rissanen has shown that there exist universal noiseless codes for {Xi} with per-letter rate redundancy as low as k/2 (log n)/n, where n is the blocklength and k is the number of source parameters. We derive an analogous result for universal quantization: for any given La-grange multiplier λ>0, there exist universal fixed-rate and variable-rate quantizers with per-letter Lagrangian redundancy (i.e., distortion redundancy plus λ times the rate redundancy) as low as λk/2 (log n)/n

Rates of convergence in adaptive universal vector quantization

We consider the problem of adaptive universal quantization. By adaptive quantization we mean quantization for which the delay associated with encoding the jth sample in a sequence of length n is bounded for all n>j. We demonstrate the existence of an adaptive universal quantization algorithm for which any weighted sum of the rate and the expected mean square error converges almost surely and in expectation as O(√(log log n/log n)) to the corresponding weighted sum of the rate and the distortion-rate function at that rate

One-pass adaptive universal vector quantization

The authors introduce a one-pass adaptive universal quantization technique for real, bounded alphabet, stationary sources. The algorithm is set on line without any prior knowledge of the statistics of the sources which it might encounter and asymptotically achieves ideal performance on all sources that it sees. The system consists of an encoder and a decoder. At increasing intervals, the encoder refines its codebook using knowledge about incoming data symbols. This codebook is then described to the decoder in the form of updates on the previous codebook. The accuracy to which the codebook is described increases as the number of symbols seen, and thus the accuracy to which the codebook is known, grows

Variable-rate source coding theorems for stationary nonergodic sources

For a stationary ergodic source, the source coding theorem and its converse imply that the optimal performance theoretically achievable by a fixed-rate or variable-rate block quantizer is equal to the distortion-rate function, which is defined as the infimum of an expected distortion subject to a mutual information constraint. For a stationary nonergodic source, however, the. Distortion-rate function cannot in general be achieved arbitrarily closely by a fixed-rate block code. We show, though, that for any stationary nonergodic source with a Polish alphabet, the distortion-rate function can be achieved arbitrarily closely by a variable-rate block code. We also show that the distortion-rate function of a stationary nonergodic source has a decomposition as the average of the distortion-rate functions of the source's stationary ergodic components, where the average is taken over points on the component distortion-rate functions having the same slope. These results extend previously known results for finite alphabets

Local moment, itinerancy and deviation from Fermi liquid behavior in Nax_xCoO2_2 for 0.71≤x≤0.840.71 \leq x \leq 0.84

Here we report the observation of Fermi surface (FS) pockets via the Shubnikov de Haas effect in Na$_x$CoO$_2$ for $x = 0.71$ and 0.84, respectively. Our observations indicate that the FS expected for each compound intersects their corresponding Brillouin zones, as defined by the previously reported superlattice structures, leading to small reconstructed FS pockets, but only if a precise number of holes per unit cell is \emph{localized}. For $0.71 \leq x < 0.75$ the coexistence of itinerant carriers and localized $S =1/2$ spins on a paramagnetic triangular superlattice leads at low temperatures to the observation of a deviation from standard Fermi-liquid behavior in the electrical transport and heat capacity properties, suggesting the formation of some kind of quantum spin-liquid ground state.Comment: 4 pages, 4 figure

Spin liquid behaviour in Jeff=1/2 triangular lattice Ba3IrTi2O9

Ba3IrTi2O9 crystallizes in a hexagonal structure consisting of a layered triangular arrangement of Ir4+ (Jeff=1/2). Magnetic susceptibility and heat capacity data show no magnetic ordering down to 0.35K inspite of a strong magnetic coupling as evidenced by a large Curie-Weiss temperature=-130K. The magnetic heat capacity follows a power law at low temperature. Our measurements suggest that Ba3IrTi2O9 is a 5d, Ir-based (Jeff=1/2), quantum spin liquid on a 2D triangular lattice.Comment: 10 pages including supplemental material, to be published in Phys. Rev. B (Rapid Comm.

Enhanced quasiparticle dynamics of quantum well states: the giant Rashba system BiTeI and topological insulators

In the giant Rashba semiconductor BiTeI electronic surface scattering with Lorentzian linewidth is observed that shows a strong dependence on surface termination and surface potential shifts. A comparison with the topological insulator Bi2Se3 evidences that surface confined quantum well states are the origin of these processes. We notice an enhanced quasiparticle dynamics of these states with scattering rates that are comparable to polaronic systems in the collision dominated regime. The Eg symmetry of the Lorentzian scattering contribution is different from the chiral (RL) symmetry of the corresponding signal in the topological insulator although both systems have spin-split surface states.Comment: 6 pages, 5 figure