Multi-Round Contention in Wireless LANs with Multipacket Reception

Multi-packet reception (MPR) has been recognized as a powerful capacity-enhancement technique for random-access wireless local area networks (WLANs). As is common with all random access protocols, the wireless channel is often under-utilized in MPR WLANs. In this paper, we propose a novel multi-round contention random-access protocol to address this problem. This work complements the existing random-access methods that are based on single-round contention. In the proposed scheme, stations are given multiple chances to contend for the channel until there are a sufficient number of ``winning" stations that can share the MPR channel for data packet transmission. The key issue here is the identification of the optimal time to stop the contention process and start data transmission. The solution corresponds to finding a desired tradeoff between channel utilization and contention overhead. In this paper, we conduct a rigorous analysis to characterize the optimal strategy using the theory of optimal stopping. An interesting result is that the optimal stopping strategy is a simple threshold-based rule, which stops the contention process as soon as the total number of winning stations exceeds a certain threshold. Compared with the conventional single-round contention protocol, the multi-round contention scheme significantly enhances channel utilization when the MPR capability of the channel is small to medium. Meanwhile, the scheme automatically falls back to single-round contention when the MPR capability is very large, in which case the throughput penalty due to random access is already small even with single-round contention

Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Korteweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the complex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.Comment: 12 figure

Quantum Phase diagram and time-of-flight absorption pictures of ultracold Bose system in a square optical superlattice

In this letter, by the use of the generalized effective potential theory, with the help of process-chain approach under the framework of Kato formulation of perturbation expansion, we calculate out the quantum phase diagram up to 8-th order for an ultracold Bose system in a square optical superlattice. Base on these perturbative data, with the help of the linear fit extrapolation technique, more accurate results are gotten, which are in excellent agreement with recent Monte-Carlo numerical results. Moreover, by employing the generalized re-summed Green's function method and cumulant expansion, the momentum distribution function of the system is also calculated analytically and the time-of-flight absorption pictures of the system are plotted.Comment: 6 pages, 6 figure

Deriving conservation laws for ABS lattice equations from Lax pairs

In the paper we derive infinitely many conservation laws for the ABS lattice equations from their Lax pairs. These conservation laws can algebraically be expressed by means of some known polynomials. We also show that H1, H2, H3, Q1, Q2, Q3 and A1 equation in ABS list share a generic discrete Riccati equation.Comment: 16 page