We show that any q-query locally decodable code (LDC) gives a copy of `1 with small distortion in the Banach space of q-linear forms on `Np1×· · ·× ` N pq , provided 1/p1 + · · ·+1/pq ≤ 1 and where k, N , and the distortion are simple functions of the code parameters. We exhibit the copies of `1 by constructing a basis directly from “smooth” LDC decoders, thus bypassing a matching lemma often u...

Image compression is concerned with reducing the amount of data needed to represent an image. Efficient image representation is achieved by exploiting the statistical and psychovisual redundancies of an image. This reported focusses on the main principles of information theory, which provides a framework for efficient signal coding from a statistical perspective. Two of the fundamental theories...

In scientific computations using floating point arithmetic, rescaling a data set multiplicatively (e.g., corresponding to a conversion from dollars to euros) changes the distribution of the mantissas, or fraction parts, of the data. A scale-distortion factor for probability distributions is defined, based on the Kantorovich distance between distributions. Sharp lower bounds are found for the sc...

We propose two efficient information hiding algorithms in the least significant bits of JPEG coefficients of images. Our algorithms embed information by modifying JPEG coefficients in such a way that the introduced distortion is minimized. We derive the expected value of the additional error due to distortion as a function of the message length and the probability distribution of the JPEG quant...

Upper and lower bounds are presented for the distortion of the optimal N -point vector quantizer applied to k-dimensional signals. Under certain smoothness conditions on the source distribution, the bounds are shown to hold for each and every value of N , the codebook size. These results extend bounds derived in the high-resolution limit, which assumes that the number of code vectors is arbitra...

Vector-Quantization (VQ) is a widely implemented method for low-bit-rate signal coding. A common assumption in the design of VQ systems is that the digital information is transmitted through a perfect channel. Under this assumption, the assignment of channel symbols to the VQ Reconstruction Vectors (RV) is of no importance. However, under physical channels, the effect of channel errors on the V...

We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion proole, ranging from symmetric or balanced to successively reenable. We present a solution to a labeling problem, which is an important part of the construction, along with a general design procedure. The high rate asymptotic performance of the quantizer is also studied....

A&r&-By defining mutual information as a maximum over an appropriate space, channel capacities can be defined as double maxima and rate-distortion functions as double minima. This approach yields valuable new insights regarding the computation of channel capacities and rate-distortion functions. In particular, it suggests a simple algorithm for computing channel capacity that consists of a mapp...

We deal with centralized and distributed rate-constrained estimation of random signal vectors performed using a network of wireless sensors (encoders) communicating with a fusion center (decoder). For this context, we determine lower and upper bounds on the corresponding distortion-rate (D-R) function. The nonachievable lower bound is obtained by considering centralized estimation with a single...