LDPC Codes – a brief Tutorial
Bernhard M.J. Leiner, Stud.ID.: 53418L
April 8, 2005
1 Introduction
Low-density parity-check (LDPC) codes are a class of li near block LDPC
codes. The name comes from the characteristic of their parity-check
matrix which contains only a few 1’s in comparison to the amount of
0’s. Their main advantage is that they provide a performance which
is very close to the capacity for a lot of different channels and linear
time complex algorithms for decoding. Furthermore are they sui ted
for implem entations that make heavy use of parallelism.
They were first introduced by Gallager in his PhD thesis in 1960. Gallager,
1960
But due to the computational effort in implementing coder and en-
coder for such codes and the introduction of Reed-Solomon codes,
they were mostly ignored until about ten years ago.
1.1 Representations for LDPC codes
Basically there are two different possibilities to represent LDPC codes.
Like all linear bl ock codes they can be described via matrices. The
second possibility is a graphical representation.
Matrix Representation
Lets look at an example for a low-density parity-check matrix first.
The matrix defined in equation (1) is a parity check matrix with di-
mension n × m for a (8, 4) code.
We can now define two numbers describing these matrix. w
r
for
the number of 1’s in each row and w
c
for the columns. For a matrix to
be called low-density the two conditions w
c
n and w
r
m must
1
