ccsds 131.0-b-2

CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODINGANNEX FTRANSFORMATION BETWEEN BERLEKAMPAND CONVENTIONAL REPRESENTATIONS(INFORMATIVE)F1PURPOSEThis annex provides information to assist users of the Reed-Solomon code in thisRecommended Standard to transform between the Berlekamp (dual basis) and Conventionalrepresentations. In addition, it shows where transformations are made to allow aconventional encoder to produce the dual basis representation on which this RecommendedStandard is based.F2TRANSFORMATIONReferring to figure F-1, it can be seen that information symbols I entering and check symbolsC emanating from the Berlekamp R-S encoder are interpreted as[z 0 , z 1 , ... , z 7 ]where the components z i are coefficients of l i , respectively:z 0 l 0 + z 1 l 1 + ... + z 7 l 7Information symbols I' entering and check symbols C' emanating from the conventional R-Sencoder are interpreted as[u 7 , u 6 , ... , u 0 ]where the components u j are coefficients of α j , respectively:u 7 α 7 + u 6 α 6 + ... + u 0A pre- and post-transformation is required when employing a conventional R-S encoder.CCSDS 131.0-B-2 Page F-1 August 2011