Set Of Packets Research Articles

Interparticipant synchronization in real-time multimedia conferencing using feedback

An algorithm related to synchronization problems arising in a multimedia multiparty conference is presented in this paper. The proposed algorithm determines the set of packets generated periodically from different participants that are arriving at a node, either for mixing at the master of a conference, or for simply playing back at a regular participant of a conference. No global synchronization of the clocks is assumed. In this paper, the statistical approach rather than the deterministic is used to determine the proper set of packets that have to be mixed at a given time. The statistics are derived from the time stamp each packet carries along with it. The essence of the proposed algorithm is to estimate the expected packet arrival time (or reference time) for each participant. With the reference time at hand, the maximum jitter and the optimum waiting time for a mixer to wait packets from all participants can be determined. By employing feedback, the proposed algorithm is shown to lead to an optimum waiting/delay time. The error of the proposed algorithm is enumerated by the Chernoff bound, demonstrated by simulation, and shown to be acceptable in practical application.

Wavelet packet based channel equalization

Recently, considerable amount of attention is being given to the field of wavelets and wavelet packets. It has found numerous applications in signal representation, image compression and applied mathematics.In this paper, we present a channel equalization method based on wavelet packets. The proposed equalizer structure is based on the fact that for sufficiently narrowband sequences, a non-ideal channel can be modelled as an attenuation and delay. If the data sequence is used to modulate a set of narrowband wavelet packets, then no equalization is required at the receiver end. The equalization problem reduces to that of determining the delay introduced by the channel for each of the wavelet packets. A minimum square variance algorithm for adaptively choosing the delay has been proposed. This algorithm has been shown to perform as desired analytically in a simple delay channel case. Simulations have been used to study its performance in the non-ideal channel’s case and the results corroborate theoretical predictions.

A synchronization algorithm for distributed multimedia environments

Network synchronization plays a significant role in transmitting multimedia objects over computer networks. Even packets from a single channel must be synchronized due to the problems in a packet switching environment, such as network jitter, frequency, and time offsets. We present an algorithm that determines the set of packets generated periodically by various participants arriving at a node. The basic advantage of the proposed algorithm is that the receiver estimates the reference times (expected arrival times of the packets) and achieves synchronization, without knowledge of the packet delays. The accuracy is improved and the complexity is reduced by predicting the time/frequency offsets between the clocks at the source and the mixer. The error is calculated by the Chernoff bound, demonstrated by simulation, and shown to be acceptable in practical applications.

A linear time erasure-resilient code with nearly optimal recovery

We develop an efficient scheme that produces an encoding of a given message such that the message can be decoded from any portion of the encoding that is approximately equal to the length of the message. More precisely, an (n,c,l,r)-erasure-resilient code consists of an encoding algorithm and a decoding algorithm with the following properties. The encoding algorithm produces a set of l-bit packets of total length cn from an n-bit message. The decoding algorithm is able to recover the message from any set of packets whose total length is r, i.e., from any set of r/l packets. We describe erasure-resilient codes where both the encoding and decoding algorithms run in linear time and where r is only slightly larger than n.

Spectral projection approach to the quantum scattering calculations

A new method of implementing scattering calculations is presented. For the S-matrix computation it produces a complete set of solutions of the wave equation that need be valid only inside the interaction region. For problems with small sizes the method is one of several that are practical in the sense that it involves merely a real symmetric Hamiltonian represented in a minimal ℒ2 basis set. For more challenging larger systems it lends itself to a very efficient time independent iterative procedure that obtains results simultaneously at all energies. A modified Chebyshev polynomial expansion of (E−Ĥ)−1 is used. This acts on a set of energy independent wave packets located on the edge of the interaction region. The procedure requires minimal storage and is shown to converge rapidly in a manner that is uniform in energy.

Greedy Packet Scheduling

Scheduling packets to be forwarded over a link is an important subtask of the routing process in both parallel computing and in communication networks. This paper investigates the simple class of greedy scheduling algorithms, namely, algorithms that always forward a packet if they can. It is first proved that for various natural classes of routes, the time required to complete the transmission of a set of packets is bounded by the number of packets, $k$, and the maximal route length, $d$, for any greedy algorithm (including the arbitrary scheduling policy). Next, tight time bounds of $d+k-1$ are proved for a specific greedy algorithm on the class of shortest paths in $n$-vertex networks. Finally, it is shown that when the routes are arbitrary, the time achieved by various natural greedy algorithms can be as bad as $\Omega(d \sqrt{k} + k)$, for any $k$, and even for $d=\Omega(n)$.

Statistical synchronization among participants in real-time multimedia conferencing

In this paper, an algorithm to determine the set of packets generated continuously and periodically from different participants that are arriving at a node either for mixing at the master of a conference, or for simply playing back at a regular participant of a conference, is proposed. The essence of the algorithm is to estimate the expected packet arrival time (or reference time) for each participant. With the reference time at hand, the maximum jitter and the optimum waiting time for a mixer to wait packets from all participants can be determined. An enhancement to improve synchronization which deals with the estimation of the time offsets between the individual periods of the sources and the period of the receiver is also presented. The error of the proposed algorithm is enumerated by the Chernoff bound and demonstrated by simulation and is shown to be acceptable in practical application. The algorithm can also be employed when traffic sources operate with different periods.

Packet routing and job-shop scheduling inO(congestion+dilation) steps

In this paper, we prove that there exists a schedule for routing any set of packets with edge-simple paths, on any network, inO(c+d) steps, wherec is the congestion of the paths in the network, andd is the length of the longest path. The result has applications to packet routing in parallel machines, network emulations, and job-shop scheduling.

Greedy Packet Scheduling on Shortest Paths

We investigate the simple class of greedy scheduling algorithms, that is, algorithms that always forward a packet if they can. Assuming that only one packet can be delivered over a link in a single step and that the routes traversed by a set of packets are distance optimal ("shortest paths"), we prove that the time required to complete transmission of a packet in the set is bounded by its route length plus the number of other packets in the set. This bound holds for any greedy algorithm, even in the ease of different starting times and different route lengths. The bound also generalizes, in the natural way, to the case in which w packets may cross a link simultaneously. Furthermore, the result holds in the asynchronous model, using the same proof technique. The generality of our result is demonstrated by a few applications. We present a simple protocol, for which we derive a general bound on the throughput with any greedy scheduling. Another protocol for the dynamic case is presented, whose packet delivery time is bounded by the length of the route of the packet plus the number of packets in the network in the time it is sent.

A note on the token distribution problem

Consider a set of packets distributed unevenly among the nodes of a bounded degree network of processors. The Token Distribution Problem involves redistributing these packets so that each node holds the same number. Token distribution algorithms underlie several efficient routing algorithms. Peleg and Upfal formulated this problem and presented a communication-efficient solution. In this paper we refine their techniques to provide a solution that is efficient with respect to both communication and local computation.

The occurrence of strong electrostatic turbulence under various experimental conditions

The Langmuir waves of a plasma can be excited through resonant interactions with a particle beam or an electromagnetic beam. For these excitations, there exist three types of phenomenology for the turbulent behavior. (1) The weak interaction regime, after a quasi-linear stage, exhibits a tendency to accumulate waves on large scales through mode couplings for which no dissipation takes place. However, intense long waves undergo a self-modulation instability, which produces a set of localized wave packets. If the beam-plasma interaction occurs along the lines of a strong magnetic field, these solitary waves are stable at some level of approximation. (2) If the interaction takes place in a moderate or negligible magnetic field, the wave packets collapse towards a point singularity in agreement with Zakharov's prediction and burn out by giving their energy to suprathermal electrons. This is the strong turbulence regime, where nonlinear self-focusing dominates over the dispersion effect. The resulting collapse produces intense spikes in the electric field at the Debye scale. This is favorable for spectroscopy involving the turbulent Stark effect. Details of the physics are reviewed, with emphasis on the various expected spectra including the distribution of suprathermal electrons that could be compared with spectroscopic data. (3) There is also an “ultrastrong” regime that has been investigated and is characterized by spikes that are so intense that the local electrostatic energy is greater than the internal energy. Spectroscopic data for this regime have recently become available from a relativistic beam-plasma experiment done at the University of California, Irvine.

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eignestates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon–Heller spectral quantization method.

The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

Techniques for Packet Voice Synchronization

Packet switching has been proposed as an effective technology for integrating voice and data in a single network. An important aspect of packet-switched voice is the reconstruction of a continuous stream of speech from the set of packets that arrive at the destination terminal, each of which may encounter a different amount of buffering delay in the packet network. The magnitude of the variation in delay may range from a few milliseconds in a local area network to hundreds of milliseconds in a long-haul packet voice and data network. This paper discusses several aspects of the packet voice synchronization problem, and techniques that can be used to address it. These techniques estimate in some way the delay encountered by each packet and use the delay estimate to determine how speech is reconstructed. The delay estimates produced by these techniques can be used in managing the flow of information in the packet network to improve overall performance. Interactions of packet voice synchronization techniques with other network design issues are also discussed.

Gauge invariant periodic quantization method

Based on the variational principle in a general manifold in the Hilbert space and the principle of gauge invariance, the general gauge invariant periodic quantization method is formulated. This method, which is a direct generalization of the one previously obtained in the case of time-dependent Hartree-Fock, leads to a quantization rule which takes the Bohr-Sommerfeld form when the variational parameters are transformed to canonical variables. The method is illustrated by applying it to the manifold of minimum wave packets for a simple harmonic oscillator. It leads to the exact energy spectrum and a discrete set of wave packets which have maximum overlap with the exact eigenstates. The method is also applied to the exact Schroedinger dynamics where it exposes some open questions of the method.

Oscillator-like coherent states of an asymmetric top

A transformation from the Euler angles to the Cayley-Klein variables is used to obtain the Schwinger boson realization of the angular momentum algebra suitable for a triaxial top. A set of wave packets for the top are then constructed in exact analogy with the oscillator coherent states. These coherent states of the top are shown to be a generalization of those defined by other authors.

Wave-wave interactions in a warm magneto-plasma

The weak non-linear interaction of a discrete set of wave packets which propagate in a warm magneto-plasma is examined within the framework of the two fluid approximation. The equations governing the behaviour of the slowly varying amplitudes of the waves are derived by applying standard perturbation theory to the combined system of Maxwell's equations and the fluid equations for each species of charged particles and by using a multiple scale expansion in both space and time. It is shown that, for arbitrary directions of propagation, the interaction matrix elements possess the familiar symmetry properties with respect to interchanges of the wave vectors of a resonant triplet. It is also verified that the mean energy and momentum of each wave can be written as the product of the wave action with omega and k respectively and that the total wave energy and momentum are conserved during an interaction.

Landau Diamagnetism from the Coherent States of an Electron in a Uniform Magnetic Field

A complete set of coherent-state wave packets has been constructed for an electron in a uniform magnetic field. These states are nonspreading packets of minimum uncertainty that follow the classical motion. Use was made of the ladder operators that generate all the eigen-states of the Hamiltonian from any one energy eigenstate. The coherent states are the eigenstates of the two ladder operators that annihilate the zero-angular-momentum ground state. We have calculated the partition function, exploiting advantages of the coherent-state basis. The Landau diamagnetism and the de Haas-van Alphen oscillations are contained in the coherent-state framework.