A lower bound for the decoder error probability of the linear MDS code

A lower bound for the decoder error probability (P sub E (u)) of a linear maximum distance separable (MDS) code is derived by counting the dominant types of decoding words around code words. It is shown that the lower bound derived is similar in form, and close numerically, to the upper bound derived

On the decoder error probability of linear codes

By using coding and combinatorial techniques, an approximate formula for the weight distribution of decodable words of most linear block codes is evaluated. This formula is then used to give an approximate expression for the decoder error probability P(sub E)(u) of linear block codes, given that an error pattern of weight u has occurred. It is shown that P(sub E)(u) approaches the constant Q as u gets large, where Q is the probability that a completely random error pattern will cause decoder error

A labeling procedure for linear finite-state codes

A method to define the labels of the state diagram of a linear finite-state code is presented and investigated. This method is particularly suitable for simple hardware implementation since it simplifies the encoder structure. The method can also be applied to the labeling of a state diagram that is not completely connected to obtain a linear finite state code with larger free distance

Locally adaptive vector quantization: Data compression with feature preservation

A study of a locally adaptive vector quantization (LAVQ) algorithm for data compression is presented. This algorithm provides high-speed one-pass compression and is fully adaptable to any data source and does not require a priori knowledge of the source statistics. Therefore, LAVQ is a universal data compression algorithm. The basic algorithm and several modifications to improve performance are discussed. These modifications are nonlinear quantization, coarse quantization of the codebook, and lossless compression of the output. Performance of LAVQ on various images using irreversible (lossy) coding is comparable to that of the Linde-Buzo-Gray algorithm, but LAVQ has a much higher speed; thus this algorithm has potential for real-time video compression. Unlike most other image compression algorithms, LAVQ preserves fine detail in images. LAVQ's performance as a lossless data compression algorithm is comparable to that of Lempel-Ziv-based algorithms, but LAVQ uses far less memory during the coding process

A comparison of the fractal and JPEG algorithms

A proprietary fractal image compression algorithm and the Joint Photographic Experts Group (JPEG) industry standard algorithm for image compression are compared. In every case, the JPEG algorithm was superior to the fractal method at a given compression ratio according to a root mean square criterion and a peak signal to noise criterion

A model for the formation of the active region corona driven by magnetic flux emergence

We present the first model that couples the formation of the corona of a solar active region to a model of the emergence of a sunspot pair. This allows us to study when, where, and why active region loops form, and how they evolve. We use a 3D radiation MHD simulation of the emergence of an active region through the upper convection zone and the photosphere as a lower boundary for a 3D MHD coronal model. The latter accounts for the braiding of the magnetic fieldlines, which induces currents in the corona heating up the plasma. We synthesize the coronal emission for a direct comparison to observations. Starting with a basically field-free atmosphere we follow the filling of the corona with magnetic field and plasma. Numerous individually identifiable hot coronal loops form, and reach temperatures well above 1 MK with densities comparable to observations. The footpoints of these loops are found where small patches of magnetic flux concentrations move into the sunspots. The loop formation is triggered by an increase of upwards-directed Poynting flux at their footpoints in the photosphere. In the synthesized EUV emission these loops develop within a few minutes. The first EUV loop appears as a thin tube, then rises and expands significantly in the horizontal direction. Later, the spatially inhomogeneous heat input leads to a fragmented system of multiple loops or strands in a growing envelope.Comment: 13 pages, 10 figures, accepted to publication in A&

Magnetic Jam in the Corona of the Sun

The outer solar atmosphere, the corona, contains plasma at temperatures of more than a million K, more than 100 times hotter that solar surface. How this gas is heated is a fundamental question tightly interwoven with the structure of the magnetic field in the upper atmosphere. Conducting numerical experiments based on magnetohydrodynamics we account for both the evolving three-dimensional structure of the atmosphere and the complex interaction of magnetic field and plasma. Together this defines the formation and evolution of coronal loops, the basic building block prominently seen in X-rays and extreme ultraviolet (EUV) images. The structures seen as coronal loops in the EUV can evolve quite differently from the magnetic field. While the magnetic field continuously expands as new magnetic flux emerges through the solar surface, the plasma gets heated on successively emerging fieldlines creating an EUV loop that remains roughly at the same place. For each snapshot the EUV images outline the magnetic field, but in contrast to the traditional view, the temporal evolution of the magnetic field and the EUV loops can be different. Through this we show that the thermal and the magnetic evolution in the outer atmosphere of a cool star has to be treated together, and cannot be simply separated as done mostly so far.Comment: Final version published online on 27 April 2015, Nature Physics 12 pages and 8 figure

Possible persistent current in a ring made of the perfect crystalline insulator

A mesoscopic conducting ring pierced by magnetic flux is known to support the persistent electron current. Here we propose possibility of the persistent current in the ring made of the perfect crystalline insulator. We consider a ring-shaped lattice of one-dimensional "atoms" with a single energy level. We express the Bloch states in the lattice as a linear combination of atomic orbitals. The discrete energy level splits into the energy band which serves as a simple model of the valence band. We show that the insulating ring (with the valence band fully filled by electrons) supports a nonzero persistent current, because each atomic orbital overlaps with its own tail when making one loop around the ring. In the tight-binding limit only the neighboring orbitals overlap. In that limit the persistent current at full filling becomes zero which is a standard result.Comment: Conference proceedings. Accepted for publication in Physica