Additive Form

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E. Sanchez-sinencio - One of the best experts on this subject based on the ideXlab platform.

  • Floating-gate analog implementation of the Additive soft-input soft-output decoding algorithm
    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003
    Co-Authors: A.f. Mondragon-torres, E. Sanchez-sinencio, K.r. Narayanan
    Abstract:

    The soft-input soft-output algorithm is used to iteratively decode concatenated codes. To efficiently implement this algorithm, an Additive Form in the logarithmic domain is employed. A novel analog implementation using CMOS translinear circuits is proposed. A multiple-input floating-gate CMOS transistor working in the subthreshold region is used as the main translinear computing element. The proposed approach allows a direct mapping between the decoding algorithm and the circuit implementation. Experimental CMOS chip results are in good agreement with theoretical and simulation results.

  • Floating gate analog implementation of the Additive soft-input soft-output decoding algorithm
    2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 2002
    Co-Authors: A.f. Mondragon-torres, E. Sanchez-sinencio
    Abstract:

    The soft-input soft-output decoding algorithm is used to decode concatenated codes iteratively. To implement this algorithm efficiently, an Additive Form in the logarithmic domain is employed. A novel analog implementation using CMOS translinear circuits is proposed. A multiple-input floating-gate CMOS transistor working in the subthreshold region is used as the main translinear computing element. The proposed approach allows a direct mapping between the decoding algorithm and the circuit implementation. Experimental CMOS chip results are in good agreement with theoretical and simulation results.

A.f. Mondragon-torres - One of the best experts on this subject based on the ideXlab platform.

  • Floating-gate analog implementation of the Additive soft-input soft-output decoding algorithm
    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003
    Co-Authors: A.f. Mondragon-torres, E. Sanchez-sinencio, K.r. Narayanan
    Abstract:

    The soft-input soft-output algorithm is used to iteratively decode concatenated codes. To efficiently implement this algorithm, an Additive Form in the logarithmic domain is employed. A novel analog implementation using CMOS translinear circuits is proposed. A multiple-input floating-gate CMOS transistor working in the subthreshold region is used as the main translinear computing element. The proposed approach allows a direct mapping between the decoding algorithm and the circuit implementation. Experimental CMOS chip results are in good agreement with theoretical and simulation results.

  • Floating gate analog implementation of the Additive soft-input soft-output decoding algorithm
    2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 2002
    Co-Authors: A.f. Mondragon-torres, E. Sanchez-sinencio
    Abstract:

    The soft-input soft-output decoding algorithm is used to decode concatenated codes iteratively. To implement this algorithm efficiently, an Additive Form in the logarithmic domain is employed. A novel analog implementation using CMOS translinear circuits is proposed. A multiple-input floating-gate CMOS transistor working in the subthreshold region is used as the main translinear computing element. The proposed approach allows a direct mapping between the decoding algorithm and the circuit implementation. Experimental CMOS chip results are in good agreement with theoretical and simulation results.

Jörg Rothe - One of the best experts on this subject based on the ideXlab platform.

  • Computational complexity and approximability of social welfare optimization in multiagent resource allocation
    Autonomous Agents and Multi-Agent Systems, 2014
    Co-Authors: Nhan-tam Nguyen, Magnus Roos, Trung Thanh Nguyen, Jörg Rothe
    Abstract:

    A central task in multiagent resource allocation, which provides mechanisms to allocate (bundles of) resources to agents, is to maximize social welfare. We assume resources to be indivisible and nonshareable and agents to express their utilities over bundles of resources, where utilities can be represented in the bundle Form, the $$k$$ k -Additive Form, and as straight-line programs. We study the computational complexity of social welfare optimization in multiagent resource allocation, where we consider utilitarian and egalitarian social welfare and social welfare by the Nash product. Solving some of the open problems raised by Chevaleyre et al. ( 2006 ) and confirming their conjectures, we prove that egalitarian social welfare optimization is $$\mathrm{NP}$$ NP -complete for the bundle Form, and both exact utilitarian and exact egalitarian social welfare optimization are $$\mathrm{DP}$$ DP -complete, each for both the bundle and the $$2$$ 2 -Additive Form, where $$\mathrm{DP}$$ DP is the second level of the boolean hierarchy over  $$\mathrm{NP}$$ NP . In addition, we prove that social welfare optimization by the Nash product is $$\mathrm{NP}$$ NP -complete for both the bundle and the $$1$$ 1 -Additive Form, and that the exact variants are $$\mathrm{DP}$$ DP -complete for the bundle and the $$3$$ 3 -Additive Form. For utility functions represented as straight-line programs, we show $$\mathrm{NP}$$ NP -completeness for egalitarian social welfare optimization and social welfare optimization by the Nash product. Finally, we show that social welfare optimization by the Nash product in the $$1$$ 1 -Additive Form is hard to approximate, yet we also give fully polynomial-time approximation schemes for egalitarian and Nash product social welfare optimization in the $$1$$ 1 -Additive Form with a fixed number of agents.

  • AAMAS - Complexity of social welfare optimization in multiagent resource allocation
    2010
    Co-Authors: Magnus Roos, Jörg Rothe
    Abstract:

    We study the complexity of social welfare optimization in multiagent resource allocation. We assume resources to be indivisible and nonshareable and agents to express their utilities over bundles of resources, where utilities can be represented in either the bundle Form or the k-Additive Form. Solving some of the open problems raised by Chevaleyre et al. [2] and confirming their conjectures, we prove that egalitarian social welfare optimization is NP-complete for both the bundle and the 1-Additive Form, and both exact utilitarian and exact egalitarian social welfare optimization are DP-complete, each for both the bundle and the 2-Additive Form, where DP is the second level of the boolean hierarchy over NP. In addition, we prove that social welfare optimization with respect to the Nash product is NP-complete for both the bundle and the 1-Additive Form. Finally, we brief y discuss hardness of social welfare optimization in terms of inapproximability.

Ran He - One of the best experts on this subject based on the ideXlab platform.

  • Robust Recovery of Corrupted Low-RankMatrix by Implicit Regularizers
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014
    Co-Authors: Ran He, Liang Wang
    Abstract:

    Low-rank matrix recovery algorithms aim to recover a corrupted low-rank matrix with sparse errors. However, corrupted errors may not be sparse in real-world problems and the relationship between ℓ1 regularizer on noise and robust M-estimators is still unknown. This paper proposes a general robust framework for low-rank matrix recovery via implicit regularizers of robust M-estimators, which are derived from convex conjugacy and can be used to model arbitrarily corrupted errors. Based on the Additive Form of half-quadratic optimization, proximity operators of implicit regularizers are developed such that both low-rank structure and corrupted errors can be alternately recovered. In particular, the dual relationship between the absolute function in ℓ1 regularizer and Huber M-estimator is studied, which establishes a connection between robust low-rank matrix recovery methods and M-estimators based robust principal component analysis methods. Extensive experiments on synthetic and real-world data sets corroborate our claims and verify the robustness of the proposed framework.

  • Half-Quadratic-Based Iterative Minimization for Robust Sparse Representation
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014
    Co-Authors: Ran He, Wei-shi Zheng
    Abstract:

    Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to perForming both error correction and error detection. More specifically, by using the Additive Form of HQ, we propose an ℓ1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative Form of HQ, we propose an ℓ1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the ℓ1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the perFormance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings.

S. Benedetto - One of the best experts on this subject based on the ideXlab platform.

  • Design and decoding of optimal high-rate convolutional codes
    IEEE Transactions on Information Theory, 2004
    Co-Authors: Graell A. I Amat, G. Montorsi, S. Benedetto
    Abstract:

    This correspondence deals with the design and decoding of high-rate convolutional codes. After proving that every (n,n-1) convolutional code can be reduced to a structure that concatenates a block encoder associated to the parallel edges with a convolutional encoder defining the trellis section, the results of an exhaustive search for the optimal (n,n-1) convolutional codes is presented through various tables of best high-rate codes. The search is also extended to find the "best" recursive systematic convolutional encoders to be used as component encoders of parallel concatenated "turbo" codes. A decoding algorithm working on the dual code is introduced (in both multiplicative and Additive Form), by showing that changing in a proper way the representation of the soft inFormation passed between constituent decoders in the iterative decoding process, the soft-input soft-output (SISO) modules of the decoder based on the dual code become equal to those used for the original code. A new technique to terminate the code trellis that significantly reduces the rate loss induced by the addition of terminating bits is described. Finally, an inverse puncturing technique applied to the highest rate "mother" code to yield a sequence of almost optimal codes with decreasing rates is proposed. Simulation results applied to the case of parallel concatenated codes show the significant advantages of the newly found codes in terms of perFormance and decoding complexity.