Lecture 30: Berlekamp-Welch algorithm

In today’s lecture, we proved the correctness of the Berlekamp Welch (BW) algorithm. See the fall 07 notes on Lecture 27 for the details. We also saw how we can use the BW algorithm, along with the “trivial” erasure decoding algorithm for RS codes, to correct from errors and erasures such that , where is the distance of the RS code. The details on this part can be found in the notes on Lecture 28. (The latter notes will be polished by next week.)

At the end of the lecture, we briefly saw how our decoding algorithm for concatenated code is losing information when the intermediate received word is fed into the unique decoder for the outer code. Next lecture, we will look at this idea in more detail.

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