Optimal Design of Multiple Description Lattice Vector Quantizers

In the design of multiple description lattice vector quantizers (MDLVQ), index assignment plays a critical role. In addition, one also needs to choose the Voronoi cell size of the central lattice v, the sublattice index N, and the number of side descriptions K to minimize the expected MDLVQ distortion, given the total entropy rate of all side descriptions Rt and description loss probability p. In this paper we propose a linear-time MDLVQ index assignment algorithm for any K >= 2 balanced descriptions in any dimensions, based on a new construction of so-called K-fraction lattice. The algorithm is greedy in nature but is proven to be asymptotically (N -> infinity) optimal for any K >= 2 balanced descriptions in any dimensions, given Rt and p. The result is stronger when K = 2: the optimality holds for finite N as well, under some mild conditions. For K > 2, a local adjustment algorithm is developed to augment the greedy index assignment, and conjectured to be optimal for finite N. Our algorithmic study also leads to better understanding of v, N and K in optimal MDLVQ design. For K = 2 we derive, for the first time, a non-asymptotical closed form expression of the expected distortion of optimal MDLVQ in p, Rt, N. For K > 2, we tighten the current asymptotic formula of the expected distortion, relating the optimal values of N and K to p and Rt more precisely.Comment: Submitted to IEEE Trans. on Information Theory, Sep 2006 (30 pages, 7 figures

Multiple Description Quantization via Gram-Schmidt Orthogonalization

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient multiple description quantization schemes is proposed in this paper. We provide a systematic treatment of the El Gamal-Cover (EGC) achievable MD rate-distortion region, and show that any point in the EGC region can be achieved via a successive quantization scheme along with quantization splitting. For the quadratic Gaussian case, the proposed scheme has an intrinsic connection with the Gram-Schmidt orthogonalization, which implies that the whole Gaussian MD rate-distortion region is achievable with a sequential dithered lattice-based quantization scheme as the dimension of the (optimal) lattice quantizers becomes large. Moreover, this scheme is shown to be universal for all i.i.d. smooth sources with performance no worse than that for an i.i.d. Gaussian source with the same variance and asymptotically optimal at high resolution. A class of low-complexity MD scalar quantizers in the proposed general framework also is constructed and is illustrated geometrically; the performance is analyzed in the high resolution regime, which exhibits a noticeable improvement over the existing MD scalar quantization schemes.Comment: 48 pages; submitted to IEEE Transactions on Information Theor

Behavioral synthesis from VHDL using structured modeling

This dissertation describes work in behavioral synthesis involving the development of a VHDL Synthesis System VSS which accepts a VHDL behavioral input specification and performs technology independent synthesis to generate a circuit netlist of generic components. The VHDL language is used for input and output descriptions. An intermediate representation which incorporates signal typing and component attributes simplifies compilation and facilitates design optimization.A Structured Modeling methodology has been developed to suggest standard VHDL modeling practices for synthesis. Structured modeling provides recommendations for the use of available VHDL description styles so that optimal designs will be synthesized.A design composed of generic components is synthesized from the input description through a process of Graph Compilation, Graph Criticism, and Design Compilation. Experiments were performed to demonstrate the effects of different modeling styles on the quality of the design produced by VSS. Several alternative VHDL models were examined for each benchmark, illustrating the improvements in design quality achieved when Structured Modeling guidelines were followed

Network vector quantization

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples

Run-time Mapping of Applications to a Heterogeneous SoC

This paper presents an iterative hierarchical approach to map an application to a parallel heterogeneous SoC architecture at run-time. The application is modeled as a set of communicating processes. The optimization objective is to minimize the energy consumption of the SoC, while still providing the required Quality of Service. This approach is flexible, scalable and the performance looks promisin

Near-Optimal Straggler Mitigation for Distributed Gradient Methods

Modern learning algorithms use gradient descent updates to train inferential models that best explain data. Scaling these approaches to massive data sizes requires proper distributed gradient descent schemes where distributed worker nodes compute partial gradients based on their partial and local data sets, and send the results to a master node where all the computations are aggregated into a full gradient and the learning model is updated. However, a major performance bottleneck that arises is that some of the worker nodes may run slow. These nodes a.k.a. stragglers can significantly slow down computation as the slowest node may dictate the overall computational time. We propose a distributed computing scheme, called Batched Coupon's Collector (BCC) to alleviate the effect of stragglers in gradient methods. We prove that our BCC scheme is robust to a near optimal number of random stragglers. We also empirically demonstrate that our proposed BCC scheme reduces the run-time by up to 85.4% over Amazon EC2 clusters when compared with other straggler mitigation strategies. We also generalize the proposed BCC scheme to minimize the completion time when implementing gradient descent-based algorithms over heterogeneous worker nodes

Hierarchical quantization indexing for wavelet and wavelet packet image coding

In this paper, we introduce the quantization index hierarchy, which is used for efficient coding of quantized wavelet and wavelet packet coefficients. A hierarchical classification map is defined in each wavelet subband, which describes the quantized data through a series of index classes. Going from bottom to the top of the tree, neighboring coefficients are combined to form classes that represent some statistics of the quantization indices of these coefficients. Higher levels of the tree are constructed iteratively by repeating this class assignment to partition the coefficients into larger Subsets. The class assignments are optimized using a rate-distortion cost analysis. The optimized tree is coded hierarchically from top to bottom by coding the class membership information at each level of the tree. Context-adaptive arithmetic coding is used to improve coding efficiency. The developed algorithm produces PSNR results that are better than the state-of-art wavelet-based and wavelet packet-based coders in literature.This research was supported by Isik University BAP-05B302 GrantPublisher's Versio

MELT - a Translated Domain Specific Language Embedded in the GCC Compiler

The GCC free compiler is a very large software, compiling source in several languages for many targets on various systems. It can be extended by plugins, which may take advantage of its power to provide extra specific functionality (warnings, optimizations, source refactoring or navigation) by processing various GCC internal representations (Gimple, Tree, ...). Writing plugins in C is a complex and time-consuming task, but customizing GCC by using an existing scripting language inside is impractical. We describe MELT, a specific Lisp-like DSL which fits well into existing GCC technology and offers high-level features (functional, object or reflexive programming, pattern matching). MELT is translated to C fitted for GCC internals and provides various features to facilitate this. This work shows that even huge, legacy, software can be a posteriori extended by specifically tailored and translated high-level DSLs.Comment: In Proceedings DSL 2011, arXiv:1109.032