Abstract:
Based on L. F. Wei's work (1984), the generalized trellis diagram oftrellis codes is defined, then the properties of rotationally invariant trellis codes with two-dimensional QAM constellations are discussed, and all the unequivalent signal assignments are given. Finally, rotationally invariant trellis codes are designed easily.

Abstract:
A simple and practical rectangular transform and the vector quantization technique are described. A method for image data compression by combining the rectangular transform with vector quantization technique is presented. By using this method, the dimension of vector coding and the size of the corresponding codebook are reduced; the vector encoding process is picked up; and also the coding rate is reduced. The results of simulation' show that this coding method is very effective in the field of image coding.

Abstract:
An isomorphism preserving Hamming weight between two algebraic geometry (AG) codes is presented to obtain the main parameters of Justesen's algebraic geometry (JAG) codes. To deduce a simple approach to the decoding algorithm, a code word in a "small" JAG code is used to correspond to error-locator polynomial. By this means, a simple decoding procedure and the ability of error correcting are explored obviously. The low and up bounds of the dimension of AG codes are also obtained.

Abstract:
In order to deduce the complexities of both the realization and coding algorithm for a given quantizer, Gersho 1 suggested two algorithms for computing nonredundant and adjacent codes of a Voronoi cell. After analyzing, we find that these algorithms are not very satisfying because they are involved in integer programming or probabilistic trial. In this paper, we present a new efficient algorithm for the corresponding problem.

Abstract:
A new mathematical model, the linear homogeneous equations with polynomial coefficients for describing the synthesis problem, is presented in this paper. It gives a nature approach ro generalize the linear synthesis to nonlinear case. This method is used ro obtain a new solution for the multisequence synthesis. The Grobner bases theory in polynomial ring is used to present an efficient algorithm for the mathematical model. This turns out to be a generalization of Euclid' algorithm. However, the new one has much brilliant prospects. As one of the important results, it is discovered that the new algorithm can be used to deduce an efficient decoding algorithm for a class of algebraic geometry codes constructed by Justesen, so the important open problem is solved.

Abstract:
This article presents a local realistic interpretation of quantum entanglement. The entanglement is explained as innate interference between the non-empty state associated with the peaked piece of one particle and the empty states associated with the non-peaked pieces of the others of entangled particles, which inseparably join together. The correlation of the results of measurements on the ensemble of composite entangled systems is related to this kind of interference. Consequently, there is no nonlocal influence between entangled particles in measurements. Particularly, this explanation thus rules out the possibility of quantum teleportation which is nowadays considered as one of cornerstones of quantum information processing. Besides, likewise, communication and computation schemes based on alleged spooky action at a distance are unlikely to be promising.

Abstract:
We have calculated the momentum distributions of nanoparticles in diffraction and interference dependent on the effective screening mass parameter or size parameter and presented the calculations for a nanoparticle inside an infinite square potential well and for a tunnelling nanoparticle through a square potential barrier. These results display the transition from quantum to classical mechanics and the simultaneous wave-particle duality of nanoparticles. The concept that the effective screening effect increases with increasing size of an object paves way for development of nanomechanics and nanotechnology.

Abstract:
We have realized that under Lorentz transformations the tick number of a moving common clock remains unchanged, that is, the hand of the clock never runs slow, but the time interval between its two consecutive ticks contracts, so the relative time has to be recorded by using the tau-clocks required by the transformations, instead of unreal slowing clocks. Thus it is argued that using rest common clocks or the equivalent the measured velocity of light emitted by a moving source, which is quasi-velocity of foreign light, is dependent of the source velocity. Nevertheless, the velocity of foreign light that should be measured by using tau-clocks is independent of the source velocity. The velocity of native light emitted by a rest source obeys the postulate of relativity in accordance with both Maxwell equations and the result of Michelson-Morley experiment. On the other hand, the velocity of foreign light obeys both Ritz's emission theory except the Lorentz factor and the postulate of constancy of light velocity if measured by using tau-clocks. Thus the emission theory does not conflict with special relativity. The present argument leads to a logical consequence that the so-called positive conclusions from experiments testing constancy of the velocity of light emitted by moving sources if using common clocks or the equivalent, instead of tau-clocks, exactly contradicts Lorentz transformations.

Abstract:
Regarding the limit hbar-->0 as the classical limit of quantum mechanics seems to be silly because hbar is a definite constant of physics, but it was successfully used in the derivation of the WKB approximation. A superseded version of the WKB approximation is proposed in the classical limit alpha-->0 where alpha=m/M is the screening parameter of an object in which m is the mass of the effective screening layer and M the total mass. This version is applicable to not only approximate solution of Schrodinger equation of a quantum particle but also that of a nanoparticle. Moreover, the version shows that the quantization rules for nanoparticles can be achieved by substituting alpha times hbar for hbar in the Bohr-Sommerfeld quantization rules of the old quantum theory. Most importantly, the version helps clarify the essential difference between classical and quantum realities and understand the transition from quantum to classical mechanics as well as quantum mechanics itself.

Abstract:
There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic explanation of quantum mechanics. The explanation implies that the tunneling particle has a certain chance to borrow enough energy from self-interference to high-jump over the barrier. The root-mean-square velocity and the effective tunneling time of an electron tunneling through a rectangular barrier are numerically calculated. No superluminal effect (Hartman effect) is found for the tunneling electron. Heisenberg's energy-time uncertainty relation for the tunneling effect is verified by calculating an introduced coefficient representing uncertainty. The present author argues that phase time, dwell time and B\"{u}tticker-Landauer time are not appropriate expressions for the actual transit time in a tunneling process. A quantum high-jumping model is presented to resolve the paradox that kinetic energy of the tunneling particle is negative and its momentum is imaginary.