Run Length Limited Error Control Codes Derived from Reed Solomon Codes

Abstract

Reed Solomon codes were standardized for numerous wireless communication systems. Most practical Reed Solomon codes belong to non-binary linear block codes defined over finite fields with characteristic two. Each linear block code contains one codeword composed of all zeros. The concatenation of this and also other codewords can lead to long, theoretically even infinite, runs of equal symbols. Such long runs do not support synchronization in wireless receivers and therefore are unwanted. In this paper it is shown that extended and some appropriately shortened Reed Solomon codes constructed over finite fields with characteristic two can be transformed into Run Length Limited Reed Solomon codes. The presented method, if applicable, allows for doing it without inserting additional redundancy. Another advantage is that after the transformation, if some round conditions are fulfilled, the decoding does not have to be rebuilt.