Rate and distortion redundancies for universal source coding with respect to a fidelity criterion

Rissanen has shown that there exist universal noiseless codes for {Xi} with per-letter rate redundancy as low as (K log N)/2N, where N is the blocklength and K is the number of source parameters. we derive an analogous result for universal source coding with respect to the squared error fidelity criterion: there exist codes with per-letter rate redundancy as low as (K log N)/2N and per-letter distortion (averaged over X^N and θ) at most D(R)[1 + K/N], where D(r) is an average distortion-rate function and K is now the number of parameters in the code

Weighted universal transform coding: universal image compression with the Karhunen-Loève transform

We introduce a two-stage universal transform code for image compression. The code combines Karhunen-Loève transform coding with weighted universal bit allocation (WUBA) in a two-stage algorithm analogous to the algorithm for weighted universal vector quantization (WUVQ). The encoder uses a collection of transform/bit allocation pairs rather than a single transform/bit allocation pair (as in JPEG) or a single transform with a variety of bit allocations (as in WUBA). We describe both an encoding algorithm for achieving optimal compression using a collection of transform/bit allocation pairs and a technique for designing locally optimal collections of transform/bit allocation pairs. We demonstrate the performance using the mean squared error distortion measure. On a sequence of combined text and gray scale images, the algorithm achieves up to a 2 dB improvement over a JPEG style coder using the discrete cosine transform (DCT) and an optimal collection of bit allocations, up to a 3 dB improvement over a JPEG style coder using the DCT and a single (optimal) bit allocation, up to 6 dB over an entropy constrained WUVQ with first- and second-stage vector dimensions equal to 16 and 4 respectively, and up to a 10 dB improvement over an entropy constrained vector quantizer (ECVQ) with a vector dimension of 4

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

Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.Comment: 12 pages, 4 figure

Empirical and Strong Coordination via Soft Covering with Polar Codes

We design polar codes for empirical coordination and strong coordination in two-node networks. Our constructions hinge on the fact that polar codes enable explicit low-complexity schemes for soft covering. We leverage this property to propose explicit and low-complexity coding schemes that achieve the capacity regions of both empirical coordination and strong coordination for sequences of actions taking value in an alphabet of prime cardinality. Our results improve previously known polar coding schemes, which (i) were restricted to uniform distributions and to actions obtained via binary symmetric channels for strong coordination, (ii) required a non-negligible amount of common randomness for empirical coordination, and (iii) assumed that the simulation of discrete memoryless channels could be perfectly implemented. As a by-product of our results, we obtain a polar coding scheme that achieves channel resolvability for an arbitrary discrete memoryless channel whose input alphabet has prime cardinality.Comment: 14 pages, two-column, 5 figures, accepted to IEEE Transactions on Information Theor

Computation of infrared cooling rates in the water vapor bands

A fast but accurate method for calculating the infrared radiative terms due to water vapor has been developed. It makes use of the far wing approximation to scale transmission along an inhomogeneous path to an equivalent homogeneous path. Rather than using standard conditions for scaling, the reference temperatures and pressures are chosen in this study to correspond to the regions where cooling is most significant. This greatly increased the accuracy of the new method. Compared to line by line calculations, the new method has errors up to 4% of the maximum cooling rate, while a commonly used method based upon the Goody band model (Rodgers and Walshaw, 1966) introduces errors up to 11%. The effect of temperature dependence of transmittance has also been evaluated; the cooling rate errors range up to 11% when the temperature dependence is ignored. In addition to being more accurate, the new method is much faster than those based upon the Goody band model

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

Polar Coding for Secret-Key Generation

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).Comment: 26 pages, 9 figures, accepted to IEEE Transactions on Information Theory; parts of the results were presented at the 2013 IEEE Information Theory Worksho