42,583 research outputs found
The Lattice of integer partitions and its infinite extension
In this paper, we use a simple discrete dynamical system to study the
integers partitions and their lattice. The set of the reachable configurations
equiped with the order induced by the transitions of the system is exactly the
lattice of integer partitions equiped with the dominance ordering. We first
explain how this lattice can be constructed, by showing its strong
self-similarity property. Then, we define a natural extension of the system to
infinity. Using a self-similar tree, we obtain an efficient coding of the
obtained lattice. This approach gives an interesting recursive formula for the
number of partitions of an integer, where no closed formula have ever been
found. It also gives informations on special sets of partitions, such as length
bounded partitions.Comment: To appear in LNCS special issue, proceedings of ORDAL'99. See
http://www.liafa.jussieu.fr/~latap
Error-resilient performance of Dirac video codec over packet-erasure channel
Video transmission over the wireless or wired network requires error-resilient mechanism since compressed video bitstreams are sensitive to transmission errors because of the use of predictive coding and variable length coding. This paper investigates the performance of a simple and low complexity error-resilient coding scheme which combines source and channel coding to protect compressed bitstream of wavelet-based Dirac video codec in the packet-erasure channel. By partitioning the wavelet transform coefficients of the motion-compensated residual frame into groups and independently processing each group using arithmetic and Forward Error Correction (FEC) coding, Dirac could achieves the robustness to transmission errors by giving the video quality which is gracefully decreasing over a range of packet loss rates up to 30% when compared with conventional FEC only methods. Simulation results also show that the proposed scheme using multiple partitions can achieve up to 10 dB PSNR gain over its existing un-partitioned format. This paper also investigates the error-resilient performance of the proposed scheme in comparison with H.264 over packet-erasure channel
Rate-distortion and complexity optimized motion estimation for H.264 video coding
11.264 video coding standard supports several inter-prediction coding modes that use macroblock (MB) partitions with variable block sizes. Rate-distortion (R-D) optimal selection of both the motion vectors (MVs) and the coding mode of each MB is essential for an H.264 encoder to achieve superior coding efficiency. Unfortunately, searching for optimal MVs of each possible subblock incurs a heavy computational cost. In this paper, in order to reduce the computational burden of integer-pel motion estimation (ME) without sacrificing from the coding performance, we propose a R-D and complexity joint optimization framework. Within this framework, we develop a simple method that determines for each MB which partitions are likely to be optimal. MV search is carried out for only the selected partitions, thus reducing the complexity of the ME step. The mode selection criteria is based on a measure of spatiotemporal activity within the MB. The procedure minimizes the coding loss at a given level of computational complexity either for the full video sequence or for each single frame. For the latter case, the algorithm provides a tight upper bound on the worst case complexity/execution time of the ME module. Simulation results show that the algorithm speeds up integer-pel ME by a factor of up to 40 with less than 0.2 dB loss in coding efficiency.Publisher's Versio
Quantum information in base n defined by state partitions
We define a "nit" as a radix n measure of quantum information which is based
on state partitions associated with the outcomes of n-ary observables and
which, for n>2, is fundamentally irreducible to a binary coding. Properties of
this measure for entangled many-particle states are discussed. k particles
specify k nits in such a way that k mutually commuting measurements of
observables with n possible outcomes are sufficient to determine the
information.Comment: 4 pages, 2 figure
- âŠ