Tailbiting codes obtained via convolutional codes with large active distance-slopes
Publikation/Tidskrift/Serie: IEEE Transactions on Information Theory
Dokumenttyp: Artikel i tidskrift
Förlag: IEEE--Institute of Electrical and Electronics Engineers Inc.
The slope of the active distances is an important parameter when investigating the error-correcting capability of convolutional codes and the distance behavior of concatenated convolutional codes. The slope of the active distances is equal to the minimum average weight cycle in the state-transition diagram of the encoder. A general upper bound on the slope depending on the free distance of the convolutional code and new upper bounds on the slope of special classes of binary convolutional codes are derived. Moreover, a search technique, resulting in new tables of rate R = 1/2 and rate R = 1/3 convolutional encoders with high memories and large active distance-slopes is presented. Furthermore, we show that convolutional codes with large slopes can be used to obtain new tailbiting block codes with large minimum distances. Tables of rate R = 1/2 and rate R = 1/3 tailbiting codes with larger minimum distances than the best previously known quasi-cyclic codes are given. Two new tailbiting codes also have larger minimum distances than the best previously known binary linear block codes with same size and length. One of them is also superior in terms of minimum distance to any previously known binary nonlinear block code with the same set of parameters.
- Electrical Engineering, Electronic Engineering, Information Engineering
- convolutional codes
- active distances
- minimum distance
- tailbiting codes
- ISSN: 0018-9448