Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
CSE545, Error Correcting Codes: Combinatorics, Algorithms and Applications
Spring 2011
Feedback Form
January 19, 2011
The purpose of this feedback form is to get an idea of the background of students in the class so that the
lectures can be prepared accor
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 14: List Decoding Capacity
October 2, 2007
Lecturer: Atri Rudra
Scribe: ThanhNhan Nguyen
In the last lecture, we stated a theorem for list decoding capacity, which we
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 15: GilbertVarshamov Bound
October 2, 2007
Lecturer: Atri Rudra
Scribe: ThanhNhan Nguyen
In the previous lectures, we have only seen upper bounds on the rate of a cod
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 16: Plotkin Bound
October 2, 2007
Lecturer: Atri Rudra
Scribe: Nathan Russell & Atri Rudra
In the last lecture we proved the GV bound, which states that for all with 0
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 17: Proof of a Geometric Lemma
October 5, 2007
Lecturer: Atri Rudra
Scribe: Sandipan Kundu & Atri Rudra
In the last lecture, we proved the Plotkin bound, except for a c
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 19: EliasBassalygo Bound
October 10, 2007
Lecturer: Atri Rudra
Scribe: Michael Pfetsch & Atri Rudra
In the last lecture, we saw the qary version of the Johnson bound
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 24: Code concatenation
October 24, 2007
Lecturer: Atri Rudra
Scribe: Yang Wang
Recall the following question we have encountered before:
Question 0.1. Is there an expli
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 25: Justesen Codes
October 26, 2007
Lecturer: Atri Rudra
Scribe: Kanke Gao
In the last lecture, we introduced code concatenation, where we compose an outer code Cout wi
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 27: BerlekampWelch Algorithm
October 31, 2007
Lecturer: Atri Rudra
Scribe: Michel Kulhandjian
In the last lecture, we discussed unique decoding of RS codes and briey w
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 29: Achieving the BSCp capacity
November 6, 2007
Lecturer: Atri Rudra
Scribe: Yang Wang & Atri Rudra
1 Derandomized GMD algorithm
We introduced the GMD algorithm in the
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 30: Achieving the BSCp capacity (II)
Tuesday, November 6, 2007
Lecturer: Atri Rudra
Scribe: Nathan Russell & Atri Rudra
In the last lecture, we started with the descrip
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 37: List Decoding of RS
November 27, 2007
Lecturer: Atri Rudra
1
Scribe: ThanhNhan Nguyen & Atri Rudra
List Decoding Recap
Recall that list decoding capacity is 1 Hq (
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 1: Introduction
August 27, 2007
Lecturer: Atri Rudra
Scribe: Atri Rudra
1 Overview
Errorcorrecting codes (or just codes) are clever ways of representing data so that o
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 13: List Decoding
October 1, 2007
Lecturer: Atri Rudra
Scribe: ThanhNhan Nguyen & Atri Rudra
In previous lectures, we have seen the following bound for unique decoding
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 12: ReedSolomon Codes
September 28, 2007
Lecturer: Atri Rudra
Scribe: Michel Kulhandjian
Last lecture we saw the proof of the Singleton bound which claims that for any
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 11: Shannon vs. Hamming
September 21,2007
Lecturer: Atri Rudra
Scribe: Kanke Gao & Atri Rudra
In the last lecture, we proved the positive part of Shannons capacity theo
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
Spring 2011
Homework 0
The problems in this homework are to help you get more comfortable with the background material.
Most of these questions would be useful in solving the real homework
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
Spring 2011
Homework 1
Due Monday, February 21, 2011 in class
You can collaborate in groups of up to 3. However, the writeups must be done individually, that
is, your group might have arr
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
Spring 2011
Homework 2
Due Monday March 7, 2011 in class
You can collaborate in groups of up to 3. However, the writeups must be done individually, that
is, your group might have arrived
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
Spring 2011
Homework 3
Due Monday, April 4, 2011 in class
You can collaborate in groups of up to 3. However, the writeups must be done individually, that
is, your group might have arrived
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 1: Introduction
August 27, 2007
Lecturer: Atri Rudra
Scribe: Atri Rudra
1 Overview
Errorcorrecting codes (or just codes) are clever ways of representing data so that o
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 2: Error Correction and Channel Noise
August 29, 2007
Lecturer: Atri Rudra
Scribe: Yang Wang & Atri Rudra
As was mentioned in the last lecture, the fundamental tradeoff
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 3: Error Correction and Distance
August 31, 2007
Lecturer: Atri Rudra
Scribe: Michael Pfetsch & Atri Rudra
The following topics were discussed in the last lecture:
Sha
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 4: Probability and Discrete Random Variables
Wednesday, January 21, 2009
Lecturer: Atri Rudra
1
Scribe: Anonymous
Counting and Probability
This lecture reviews elementa
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 4: Hamming code and Hamming bound
September 5,2007
Lecturer: Atri Rudra
Scribe: Kanke Gao & Atri Rudra
In the last couple of lectures, we have seen that the repetition
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 5: Linear Codes
September 7, 2007
Lecturer: Atri Rudra
Scribe: Michel Kulhandjian & Atri Rudra
Last lecture we talked about the Hamming bound (for the special case of d
Error Correcting Codes: Combinatorics, Algorithms and Applications
CSE 545

Spring 2011
Error Correcting Codes: Combinatorics, Algorithms and Applications
(Fall 2007)
Lecture 6: General Hamming Codes
September 10, 2007
Lecturer: Atri Rudra
Scribe: Nathan Russell
In the last lecture, we saw the following ways of dening an [n, k, d]q linear co