A New Perspective of Cyclicity in Convolutional Codes

作者：Gomez Torrecillas Jose^*; Lobillo F J^*; Navarro Gabriel^*

来源：IEEE Transactions on Information Theory, 2016, 62(5): 2702-2706.

DOI：10.1109/TIT.2016.2538264

• Convolutional codes
• cyclic convolutional codes
• rational functions
• Ore polynomials
• finite fields

In this paper, we propose a new way of providing cyclic structures to convolutional codes. We define the skew cyclic convolutional codes as left ideals of a quotient ring of a suitable non-commutative polynomial ring. In contrast to the previous approaches to cyclicity for convolutional codes, we use Ore polynomials with coefficients in a field (the rational function field over a finite field), so their arithmetic is very well known and we may proceed similarly to cyclic block codes. In particular, we show how to obtain easily skew cyclic convolutional codes of a given dimension, and we compute an idempotent generator of the code and its dual.

• 出版日期2016-5