ccsds 131.0-b-2

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CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODINGANNEX EINFORMATIVE REFERENCES(INFORMATIVE)[E1] Procedures Manual for the Consultative Committee for Space Data Systems. CCSDSA00.0-Y-9. Yellow Book. Issue 9. Washington, D.C.: CCSDS, November 2003.[E2] Telemetry Channel Coding. Recommendation for Space Data System Standards,CCSDS 101.0-B-6-S. Historical Recommendation. Issue 6-S. Washington, D.C.:CCSDS, (October 2002) August 2005.[E3] Advanced Orbiting Systems, Networks and Data Links: Architectural Specification.Recommendation for Space Data System Standards, CCSDS 701.0-B-3-S. HistoricalRecommendation. Issue 3-S. Washington, D.C.: CCSDS, (June 2001) August 2005.[E4] M. Perlman and J. Lee. Reed-Solomon Encoders—Conventional vs. Berlekamp’sArchitecture. JPL Publication 82-71. Pasadena, California: NASA-Jet PropulsionLaboratory, December 1982.[E5] Mission Profiles for TM Synchronization and Channel Coding. ProposedRecommendation for Space Data System Practices, CCSDS 131.4-W-0. White Book.Issue 0. Washington, D.C.: CCSDS, Proposed.NOTE – Normative references are listed in 1.7.CCSDS <strong>131.0</strong>-B-2 Page E-1 August 2011
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 <strong>131.0</strong>-B-2 Page F-1 August 2011
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ccsds 131.0-b-2

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