Posted by: atri | October 29, 2007

## Lecture 26: Decoding Concatenated codes

In today’s lecture we saw how to decode concatenated codes up to $\frac{1}{4}$th of their design distance in polynomial time (assuming that the outer code can be decoded up to half its distance in polynomial time).

We stated the Berlekamp-Welch algorithm for such an unique decoder for Reed-Solomon codes. Next lecture, we will prove the correcteness of the algorithm along with some generalizations to error correction from a mixture of errors and erasures (which in turn will be useful for designing efficient algorithms to decode certain concatenated codes up to half their design distance).