Reed Solomon Encoder/Decoder on the StarCore SC140/SC1400 Cores, With Extended Examples

1 Basics of Forward Error Correction (FEC) .............2 2 Theory ..................................................................... 3 2.1 Galois Fields ........................................................... 3 2.2 Reed-Solomon Codes ..............................................6 2.3 Error-Correcting Performance of Reed-Solomon Codes ..............................................9 3 SC140 Core Overview ..........................................10 4 Implementation on the SC140 Core.......................12 4.1 Polynomial Evaluation Over GF(256) .................. 13 4.2 MAC Instructions Over Galois Fields ..................14 4.3 Look-up Tables .....................................................14 4.4 Lowest Cycle Count Limit for Polynomial Evaluation .............................................................15 4.5 Cycle Count of the Reed-Solomon Routines ........16 5 Results ................................................................... 17 6 Summary ............................................................... 19 7 References .............................................................19 Reed Solomon Encoder/Decoder on the StarCoreTM SC140/SC1400 Cores, With Extended Examples