Posted by: atri | April 13, 2009

## Lecture 33: Achieving the BSC capacity

In Friday’s lecture, we saw an explicit code that achieves the $BSC_p$ capacity with polynomial time encoding and decoding algorithms. The code is a concatenated code where the outer code is a binary code that achieves the Zyablov bound (and can be decoded up to half the Zyablov bound) and the inner code is a code that achieves the $BSC_p$ capacity (we find such a code via a brute force search). This material appears in the scribed notes for Lecture 29 and Lecture 30 from Fall 07.

In Monday’s lecture, we’ll mention a question concerning achieving the BSC capacity that is still open to this day. Then we will move on to expander codes.