randLDPC -- low density parity check matrix

Synopsis

Usage:

randLDPC(n, k, m, b)
Inputs:
- n, an integer,
- k, an integer,
- m, a real number,
- b, an integer,
Outputs:
- a matrix, $H$

Description

The parameter n indicates the number of columns of $H$. The number of rows of $H$ is n-k. The real number m indicates the slope of the line which relates n and the number of ones in $H$. Finally, b indicates the constant term of the line which relates $n$ and the number of ones in $H$. The number of ones in $H$ is determined by the formula floor(n*m) + b. Since this formula is linear in the number of columns of $H$, randLDPC produces a sparse matrix, for a fixed set of parameters n, k, m and b.

i1 : randLDPC(15,5,3.0,0)

o1 = | 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 |
     | 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 |
     | 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 |
     | 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 |
     | 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 |
     | 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 |
     | 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 |
     | 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 |
     | 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 |
     | 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 |

                  10           15
o1 : Matrix (GF 2)   <-- (GF 2)

Ways to use randLDPC :

randLDPC(ZZ,ZZ,RR,ZZ)

For the programmer

The object randLDPC is a method function.