Reed Solomon Decoder - Computation Structures Group

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Error Correction Code ● Add parity so that corrupted messages are closest to the original signal with a given distance metric. ● Corrupt messages fail to meet some criterion, labeling them corrupt ● Search the space around corrupt messages for the nearest (most likely) original message ● Search space is huge. Decoding is intractable in general ● Error Correcting Codes designed to make decoding search feasible 4
A Brief Word About Math ● Based on Galois Field 2 8 (256) arithmetic ● Symbols encode polynomial coefficients 173=8b10101101=x 7 x 5 x 3 x 2 x 0 ● Arithmetic is modulo the primitive polynomial – Addition is bitwise modulo 2 (XOR) – General Multiplication is polynomial multiplication modulo the primitive polynomial – Multiplication by roots of primitive polynomial is particularly easy because x is a root – General case inversion is difficult 5
Page 1 and 2: Reed Solomon Decoder 6.375 Final Pr
Page 3: Reed Solomon Applications ● Space
Page 7 and 8: Galois Field Multiplication ● Mul
Page 9 and 10: Galois Field Inversion ● The inve
Page 11 and 12: Reed Solomon Decoder Concept ● Th
Page 13 and 14: Syndrome Calculator ri Byte shift r
Page 15 and 16: Berlekamp Algorithm ● Calculates
Page 17 and 18: Verification & Testing ● Individu
Page 19 and 20: 0 254 932 Data block input Syndrome
Page 21 and 22: Buffer Design Exploration ● Buffe
Page 23 and 24: Synthesis and Layout Module Area (m
Page 25 and 26: Conclusions ● Reed Solomon decode

Reed Solomon Decoder - Computation Structures Group

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