593 research outputs found
On Quadratic Inverses for Quadratic Permutation Polynomials over Integer Rings
An interleaver is a critical component for the channel coding performance of
turbo codes. Algebraic constructions are of particular interest because they
admit analytical designs and simple, practical hardware implementation. Sun and
Takeshita have recently shown that the class of quadratic permutation
polynomials over integer rings provides excellent performance for turbo codes.
In this correspondence, a necessary and sufficient condition is proven for the
existence of a quadratic inverse polynomial for a quadratic permutation
polynomial over an integer ring. Further, a simple construction is given for
the quadratic inverse. All but one of the quadratic interleavers proposed
earlier by Sun and Takeshita are found to admit a quadratic inverse, although
none were explicitly designed to do so. An explanation is argued for the
observation that restriction to a quadratic inverse polynomial does not narrow
the pool of good quadratic interleavers for turbo codes.Comment: Submitted as a Correspondence to the IEEE Transactions on Information
Theory Submitted : April 1, 2005 Revised : Nov. 15, 200
An Analysis of the Connections Between Layers of Deep Neural Networks
We present an analysis of different techniques for selecting the connection
be- tween layers of deep neural networks. Traditional deep neural networks use
ran- dom connection tables between layers to keep the number of connections
small and tune to different image features. This kind of connection performs
adequately in supervised deep networks because their values are refined during
the training. On the other hand, in unsupervised learning, one cannot rely on
back-propagation techniques to learn the connections between layers. In this
work, we tested four different techniques for connecting the first layer of the
network to the second layer on the CIFAR and SVHN datasets and showed that the
accuracy can be im- proved up to 3% depending on the technique used. We also
showed that learning the connections based on the co-occurrences of the
features does not confer an advantage over a random connection table in small
networks. This work is helpful to improve the efficiency of connections between
the layers of unsupervised deep neural networks
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