A Continuous-Time Recurrent Neural Network for Joint Equalization and Decoding – Analog Hardware Implementation Aspects

Equalization and channel decoding are “traditionally” two cascade processes at the receiver side of a digital transmission. They aim to achieve a reliable and efficient transmission. For high data rates, the energy consumption of their corresponding algorithms is expected to become a limiting factor. For mobile devices with limited battery’s size, the energy consumption, mirrored in the lifetime of the battery, becomes even more crucial. Therefore, an energy-efficient implementation of equalization and decoding algorithms is desirable. The prevailing way is by increasing the energy efficiency of the underlying digital circuits. However, we address here promising alternatives offered by mixed (analog/digital) circuits. We are concerned with modeling joint equalization and decoding as a whole in a continuous-time framework. In doing so, continuous-time recurrent neural networks play an essential role because of their nonlinear characteristic and special suitability for analog very-large-scale integration (VLSI). Based on the proposed model, we show that the superiority of joint equalization and decoding (a well-known fact from the discrete-time case) preserves in analog. Additionally, analog circuit design related aspects such as adaptivity, connectivity and accuracy are discussed and linked to theoretical aspects of recurrent neural networks such as Lyapunov stability and simulated annealing

Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit Systems

A relationship between a recently introduced multipartite entanglement measure, state mixedness, and spin-flip symmetry is established for any finite number of qubits. It is also shown that, within those classes of states invariant under the spin-flip transformation, there is a complementarity relation between multipartite entanglement and mixedness. A number of example classes of multiple-qubit systems are studied in light of this relationship.Comment: To appear in Physical Review A; submitted 14 May 200