# Additive Form - Explore the Science & Experts | ideXlab

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The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform

### E. Sanchez-sinencio – 1st expert 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 – 2nd expert 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 – 3rd expert 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.