# Introduction to coding theory (CMU, Spr 2010)

## January 13, 2010

### Lecture 1 summary

Filed under: Lecture summary — Venkat Guruswami @ 4:42 pm

In today’s lecture, we discussed some administrative aspects concerning problem sets and scribing. (For those who are taking the class for credit and couldn’t make it to lecture today,  I expect there will be about 3 problem sets that can be solved and written up in pairs, and each student will be responsible for scribing in detail lectures for one week starting in about two weeks.)

We discussed some historical context of Shannon’s and Hamming’s work, informally stated the nosieless and noisy coding theorems of Shannon (a formal statement and proof of the latter for a special channel will be covered probably next week), introduced the length 7 Hamming code, made a few basic definitions (Hamming distance, rate, distance, etc.), and argued why distance combinatorially captures  the error/erasure correcting capabilities of codes. There was discussion led by student questions/comments about using the fact that an error-correcting decoder also recovers the identity of error locations to limit the rate of ${t}$-error-correcting codes, leading to the Hamming/Volume upper bound on rate.