We derive a relationship between network representation in energy-efficient neuromorphic architectures and block Toplitz convolutional matrices. Inspired by this connection, we develop deep convolutional networks using a family of structured convolutional matrices and achieve state-of-the-art trade-off between energy efficiency and classification accuracy for well-known image recognition tasks....

| It is well known that a convolutional code is essentially a linear system deened over a nite eld. In this paper we elaborate on this connection. We will deene convolutional codes as the dual of a complete linear behavior in the sense of Willems. Using ideas from systems theory we describe a set of generalized rst order descriptions for convolutional codes. As an application of these ideas, we...

In this paper, starting with a family of convolutional codes, we construct a new convolutional code and we introduce also necessary and sufficient conditions in order that the new convolutional code is MDS.

Abstract—The free distance of (n, k, l) convolutional codes has some connection with the memory length, which depends on not only l but also on k. To efficiently obtain a large memory length, we have constructed a new class of (2k, k, l) convolutional codes by (2k, k) block codes and (2, 1, l) convolutional codes, and its encoder and generation function are also given in this paper. With the he...

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the “best” recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error p...

We describe how to train a two-layer convolutional Deep Belief Network (DBN) on the 1.6 million tiny images dataset. When training a convolutional DBN, one must decide what to do with the edge pixels of teh images. As the pixels near the edge of an image contribute to the fewest convolutional lter outputs, the model may see it t to tailor its few convolutional lters to better model the edge pix...

Maximum-distance separable (MDS) convolutional codes are characterized through the property that the free distance attains the generalized Singleton bound. The existence of MDS convolutional codes was established by two of the authors by using methods from algebraic geometry. This correspondence provides an elementary construction of MDS convolutional codes for each rate and each degree . The c...

A double serially concatenated code with two interleaves consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits and an inner encoder whose input words are the permuted middle codewords. The construction can be generalized to h cascaded encoders separated by h – 1 interleavers, where ...