Posted by: atri | December 3, 2007

Lecture 40: Folded Reed-Solomon Codes

In today’s lecture we finished talking about list recovery and soft decoding of RS codes. We then defined folded RS codes and saw an intuition for why these new codes might help push the fraction of errors beyond $1-\sqrt{R}$. I might have gone a bit fast on some portions of the lecture. Please use the comments section if you have any questions.

Next lecture, we will present a list decoding algorithm for folded RS codes and delve into its analysis. We will be using a bit of extension fields, so this is a good time to brush up your knowledge about them and irreducible polynomials. Actually, we will just use the fact that $\mathbb{F}_q[X]/E(X)$, where $E(X)$ is an irreducible polynomial of degree $k$ is the field $\mathbb{F}_{q^k}$. The notation $\mathbb{F}_q[X]/E(X)$ denotes all polynomials with coefficients from $\mathbb{F}_q$ modulo the polynomial $E(X)$.