Galois Fields for Digital Image and Signal Processing: Evidence for the Importance of Field Specificity

Abstract

It is shown that any digital signal and image processing algorithms can be reduced to multivalued logic operations. The basis for this is signal models, in which each discrete level is associated with an element of the Galois field. Therefore, the development of algorithms and computing systems operating directly in Galois fields is topical. To simplify the calculation of products in Galois fields, in turn, it is convenient to pass from an element of the Galois field to the degree of a primitive element that defines this element. This allows the multiplication operation to be reduced to the addition operation. A specific example of an algorithm and a block diagram of a device that implements it, which allows such a reduction, are presented. This example demonstrates that for solving problems of digital signal and image processing, it is very important to take into account the specifics of specific Galois fields.