Standard array

Abstract: Decoding random linear codes is a well studied problem with many applications in complexity theory and cryptography. The security of almost all coding and LPN/LWE-based schemes relies on the assumption that it is hard to decode random linear codes. Recently, there has been progress in improving the running time of the best decoding algorithms for binary random codes. The ball collision technique of Bernstein, Lange and Peters lowered the complexity of Stern's information set decoding algorithm to 20.0556n. Using representations this bound was improved to 20.0537n by May, Meurer and Thomae. We show how to further increase the number of representations and propose a new information set decoding algorithm with running time 20.0494n.

Abstract: We propose a new decoding algorithm for random binary linear codes. The so-called information set decoding algorithm of Prange (1962) achieves worst-case complexity \(2^{0.121n}\). In the late 80s, Stern proposed a sort-and-match version for Prange’s algorithm, on which all variants of the currently best known decoding algorithms are build. The fastest algorithm of Becker, Joux, May and Meurer (2012) achieves running time \(2^{0.102n}\) in the full distance decoding setting and \(2^{0.0494n}\) with half (bounded) distance decoding.

Abstract: An image is partitioned into cells of pxp pixels. Each cell is regarded as a vector of dimension p2and is encoded by searching through a codebook for a nearest matching representative vector. A binary word identifying the selected representative vector is assigned as the codeword to describe the original cell. The decoder uses this codeword to address a codebook. Each entry of the codebook contains a full precision digital representation of one of the N representative vectors. The codebook design is based on a clustering technique for vector quantizer design preceded by a classification of training cells into edge or shade cells. Results for coding rates from 0.5 to 1.5 bits/pixel are discussed. Vector quantization appears to be a powerful and promising technique for image coding.

Abstract: The problem of locating signals transmitted in the proximity of an antenna array has been studied extensively in the signal processing literature. In this paper, we consider the standard array manifold models used in these works and show that they differ, sometimes significantly, from the model based on electromagnetic theory. In particular, the standard models do not correspond to the equations governing an electromagnetic field near an antenna or an array. They also do not take into account the characteristics of the near-field source, such as the type and orientation of the transmitting antenna, which may have a profound impact on the signals received by the array. We use selected numerical examples based on a numerical electromagnetic code to illustrate the various issues raised herein.