KONSTRUKSI KODE KONVOLUSIONAL MELALUI PENDEKATAN SISTEM LINEAR; CONSTRUCTION OF CONVOLUTIONAL CODES VIA LINEAR SYSTEM APPROACH

RICKY ADITYA, Ari Suparwanto

2011 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

We discuss about construction of convolutional codes via linear system approach. The main discussion in coding theory is error-correcting codes. The ability of a code to detect and correct errors which might occur in a message transmission is determined by its minimum distance. One class of codes which is often studied is linear block codes, which is based on vector spaces over a finite field. There are some limitedness in linear block codes such that their error-correcting process is not optimal. Convolutional codes is a developing of linear block codes, which is based on free modules over principal ideal domain. The concept of convolutional codes is principally same as the linear block codes, by some generalizations using polynomial representation. The concept of free distance in convolutional codes is also a generalization of the concept of minimum distance in linear block codes. Moreover, free distance of a convolutional code might be large enough, depend on its complexity, so that its error-correcting process can be more optimal. We give first the basic concepts of convolutional codes, including the basic definition, encoding and decoding. Then we present the representation of convolutional codes as discrete time-invariant linear system with its properties. Moreover, some construction techniques of convolutional codes using the representation system is discussed, especially the construction techniques such that the constructed codes have large free distance will be discussed.

Kata Kunci : sistem linear