April 8, 2004
18.413: Error-Correcting Codes Lab
Lecture 16
Lecturer: Daniel A. Spielman
16.1
Related Reading
Fan, pp. 108110.
Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative De
coding, by S. Benedetto, D. Divsa
March 18, 2004
18.413: Error-Correcting Codes Lab
Lecture 13
Lecturer: Daniel A. Spielman
13.1
Related Reading
Ecient Erasure Correcting Codes, from Stellar web page. Im not suggesting that you
read this paper right now. But, this is where the material
April 6, 2004
18.413: Error-Correcting Codes Lab
Lecture 15
Lecturer: Daniel A. Spielman
15.1
Related Reading
Fan, pp. 108110.
15.2
Remarks on Convolutional Codes
Most of this lecture will b e devoted to Turbo codes and their variants. However, since the
April 1, 2004
18.413: Error-Correcting Codes Lab
Lecture 14
Lecturer: Daniel A. Spielman
14.1
Related Reading
Fan, pp. 97105.
14.2
Convolutional Codes
This lecture, and small project 3, is about convolutional codes. Convolutional codes are classical,
and
March 11, 2004
18.413: Error-Correcting Codes Lab
Lecture 11
Lecturer: Daniel A. Spielman
11.1
Related Reading
Fan, Chapter 2, Sections 3 and 4.
11.2
Belief Propagation on Trees
Lets consider the case of low-density parity-check codes when the underlying
18.413: ErrorCorrecting Codes Lab
March 16, 2004
Lecture 12
Lecturer: Daniel A. Spielman
12.1
Representing Probabilities, Equality nodes
It turns out that probabilities are not always the best way to represent the quantities we are
considering. To see why
18.413: ErrorCorrecting Codes Lab
February 24, 2004
Lecture 6
Lecturer: Daniel A. Spielman
6.1
Introduction
Begin by describing LDPC codes, and how they are described by many local constraints. Point out
that random graphs locally look like trees (from th
18.413: ErrorCorrecting Codes Lab
March 2, 2004
Lecture 8
Lecturer: Daniel A. Spielman
8.1
Vector Spaces
A set C cfw_0, 1n is a vector space if for all x C and y C , x + y C , where we take addition
to be componentwise modulo 2. We note that over 0, 1, we
18.413: ErrorCorrecting Codes Lab
February 26, 2004
Lecture 7
Lecturer: Daniel A. Spielman
To begin, let me point out that there was a typo in the lecture notes from last lecture. Lemma 6.4.1
should have said:
Lemma 7.0.1.
Pext [X1 = a1 |Y2 Y3 = b2 b3 ] =
18.413: ErrorCorrecting Codes Lab
March 4, 2004
Lecture 9
Lecturer: Daniel A. Spielman
9.1
Related Reading
Fan, Chapter 2, Sections 3 and 4.
Programming Tips #10: Working with GF (2) matrices.
9.2
LDPC Codes
We will examine the simplest and most natural