This semitutorial paper starts with a review of some of Fomey’s contributions on the algebraic structure of convolutional encoders on which some new results on minimal convolutional encoders rest. An example is given of a basic convolutional encoding matrix whose number of abstract states is minimal over all equivalent encoding matrices. However, this encoding matrix can be realized with a mini...

The paper addresses minimality of encoders for basic convolutional codes over Zpr by using a recently developed concept of row reducedness for polynomial matrices over Zpr . It is known in the literature that the McMillan degree of a basic encoder is an upper bound for the minimum number of trellis states, but a general expression is missing. This open problem is solved in this paper. An expand...

This paper concerns to blind identification of a convolutional code with desired rate in a noiseless transmission scenario. To the best of our knowledge, blind estimation of convolutional code based on only the received bitstream doesn’t lead to a unique solution. Hence, without loss of generality, we will assume that the transmitter employs a non-catastrophic encoder. Moreover, we consider a c...

We address the concept of “minimal polynomial encoder” for finite support linear convolutional codes over Zpr . These codes can be interpreted as polynomial modules which enables us to apply results from the 2007-paper [8] to introduce the notions of “p-encoder” and “minimal p-encoder”. Here the latter notion is the ring analogon of a row reduced polynomial encoder from the field case. We show ...

Quantum convolutional codes, like their classical counterparts, promise to offer higher error correction performance than block codes of equivalent encoding complexity, and are expected to find important applications in reliable quantum communication where a continuous stream of qubits is transmitted. Grassl and Roetteler devised an algorithm to encode a quantum convolutional code with a “pearl...

Electrical drives frequently use incremental encoders as position sensor. The paper deals with the modeling and simulation of an incremental encoder and associated units for processing the information provided by the encoder. A mathematical model of the incremental encoder is presented. Based on encoder signals the direction of the rotation, the position and the speed are identified. The descri...

This paper tackles the reduction of redundant repeating generation that is often observed in RNN-based encoder-decoder models. Our basic idea is to jointly estimate the upper-bound frequency of each target vocabulary in the encoder and control the output words based on the estimation in the decoder. Our method shows significant improvement over a strong RNN-based encoder-decoder baseline and ac...