An Efficient Mode Decision Algorithm Based on Dynamic Grouping and Adaptive Adjustment for H.264/AVC

“This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder." “Copyright IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.”The rate distortion optimization (RDO) enabled mode decision (MD) is one of the most important techniques introduced by H.264/AVC. By adopting the exhaustive calculation of rate distortion, the optimal MD enhances the video encoding quality. However, the computational complexity is significantly increased, which is a key challenge for real-time and low power consumption applications. This paper presents a new fast MD algorithm for highly efficient H.264/AVC encoder. The proposed algorithm employs a dynamic group of candidate inter/intra modes to reduce the computational cost. In order to minimize the performance loss incurred by improper mode selection for the previously encoded frames, an adaptive adjustment scheme based on the undulation of bitrate and PSNR is suggested. Experimental results show that the proposed algorithm reduces the encoding time by 35% on average, and the loss of PSNR is usually limited in 0.1 dB with less than 1% increase of bitrate

A modified particle method for semilinear hyperbolic systems with oscillatory solutions

We introduce a modified particle method for semi-linear hyperbolic systems with highly oscillatory solutions. The main feature of this modified particle method is that we do not require different families of characteristics to meet at one point. In the modified particle method, we update the ith component of the solution along its own characteristics, and interpolate the other components of the solution from their own characteristic points to the ith characteristic point. We prove the convergence of the modified particle method essentially independent of the small scale for the variable coefficient Carleman model. The same result also applies to the non-resonant Broadwell model. Numerical evidence suggests that the modified particle method also converges essentially independent of the small scale for the original Broadwell model if a cubic spline interpolation is used

An efficient fast mode decision algorithm for H.264/AVC intra/inter predictions

H.264/AVC is the newest video coding standard, which outperforms the former standards in video coding efficiency in terms of improved video quality and decreased bitrate. Variable block size based mode decision (MD) with rate distortion optimization (RDO) is one of the most impressive new techniques employed in H.264/AVC. However, the improvement on performance is achieved at the expense of significantly increased computational complexity, which is a key challenge for real-time applications. An efficient fast mode decision algorithm is then proposed in this paper. By exploiting the correlation between macroblocks and the statistical characteristics of sub-macroblock in MD, the video encoding time can be reduced 52.19% on average. Furthermore, the motion speed based adjustment scheme was introduced to minimize the degradation of performanc

Chapman-Enskog expansion of the Boltzmann equation and its diagrammatic interpretation

We perform a Chapman-Enskog expansion of the Boltzmann equation keeping up to quadratic contributions. We obtain a generalized nonlinear Kubo formula, and a set of integral equations which resum ladder and extended ladder diagrams. We show that these two equations have exactly the same structure, and thus provide a diagrammatic interpretation of the Chapman-Enskog expansion of the Boltzmann equation, up to quadratic order.Comment: 5 pages, 2 figures in eps, talk given at XXXI International Symposium on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. URL http://ismd31.ccnu.edu.cn

Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries

A rigorous convergence result is given for a projection scheme for the Navies–Stokes equations in the presence of boundaries. The numerical scheme is based on a finite-difference approximation, and the pressure is chosen so that the computed velocity satisfies a discrete divergence-free condition. This choice for the pressure and the particular way that the discrete divergence is calculated near the boundary permit the error in the pressure to be controlled and the second-order convergence in the velocity and the pressure to the exact solution to be shown. Some simplifications in the calculation of the pressure in the case without boundaries are also discussed

Pathwise Performance of Debt Based Policies for Wireless Networks with Hard Delay Constraints

Hou et al have introduced a framework to serve clients over wireless channels when there are hard deadline constraints along with a minimum delivery ratio for each client's flow. Policies based on "debt," called maximum debt first policies (MDF) were introduced, and shown to be throughput optimal. By "throughput optimality" it is meant that if there exists a policy that fulfils a set of clients with a given vector of delivery ratios and a vector of channel reliabilities, then the MDF policy will also fulfill them. The debt of a user is the difference between the number of packets that should have been delivered so as to meet the delivery ratio and the number of packets that have been delivered for that client. The maximum debt first (MDF) prioritizes the clients in decreasing order of debts at the beginning of every period. Note that a throughput optimal policy only guarantees that \begin{small} \liminf_{T \to \infty} \frac{1}{T}\sum_{t=1}^{T} \mathbbm{1}\{\{client n$'s packet is delivered in frame$t} \} \geq q_{i} \end{small}, where the right hand side is the required delivery ratio for client $i$. Thus, it only guarantees that the debts of each user are $o(T)$, and can be otherwise arbitrarily large. This raises the interesting question about what is the growth rate of the debts under the MDF policy. We show the optimality of MDF policy in the case when the channel reliabilities of all users are same, and obtain performance bounds for the general case. For the performance bound we obtain the almost sure bounds on $\limsup_{t\to\infty}\frac{d_{i}(t)}{\phi(t)}$ for all $i$, where $\phi(t) = \sqrt{2t\log\log t}$