Intuitive Estimation of the Number of Error Correction Bits

Introduction Hamming Distance Intuitive Estimation of Error Correction Bits Digging Deeper Comparing against BCH Codes What about Reed-Solomon Codes? BCH vs Reed-Solomon Codes References Footnotes Introduction I’ve been interested in error correcting codes (ECC) for a while now, and though I haven’t gotten very far, I keep on reading and, occasionally, writing about it. Except for really simple schemes, ECC theory gets complicated quickly. The two codes that I’ve looked at most are Reed-Solomon (RS) and binary Bose–Chaudhuri–Hocquenghem (BCH) codes. They are closely related: both use polynomial math that is normally performed over a Galois Field, though, as shown in my earlier Reed-Solomon blog post, that’s not strictly required. The encoding algorithms are relatively straightforward but the decoding algorithms are significantly more complicated. RS and binary BCH codes differ in the size of their symbols, their alphabet: a symbol of the former consists of multiple bits, often 8 bits,…

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