An optimal control theory for sys - tems de ned over nite rings
نویسنده
چکیده
A fundamental problem of coding theory is the e cient decoding of certain classes of convolutional codes. It would be highly desirable to develop e cient algorithms which are capable of decoding classes of convolutional codes with particular algebraic properties. In this article we do formulate the problem in terms of linear systems theory and we show that the posed question is connected to some classical problems of systems theory. A convolutional code can be viewed as a discrete time linear system de ned over a nite eld F and we will say more about it in Section 2. Sometimes it is too restrictive to work over a nite eld F and because of this several authors did recently consider codes over a nite ring R (such as the ring Zq consisting of the integers modulo q e.g.) or even codes over arbitrary nite groups (see e.g. [3]). Convolutional codes are widely used in the transmission of data over noisy channels. In conjunction with data compression and modulation schemes they are nowadays integral part of many communication devices. As an example we want to mention the transmission of pictures and other data from deep space, where NASA has used convolutional codes in a most successful way. In the literature one can nd several decoding algorithms. Probably the most widely implemented algorithm is the Viterbi decoding algorithm and we refer to the textbooks [2, 13] for details. Under some natural assumption
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تاریخ انتشار 1998