gen2par - Convert between parity-check and generator matrices

Syntax

parmat = gen2par(genmat) genmat = gen2par(parmat)

Description

parmat = gen2par(genmat) converts the standard-form binary generator matrix genmat into the corresponding parity-check matrix parmat.

genmat = gen2par(parmat) converts the standard-form binary parity-check matrix parmat into the corresponding generator matrix genmat.

The standard forms of the generator and parity-check matrices for an [n,k] binary linear block code are shown in the table below

Type of Matrix	Standard Form	Dimensions
Generator	[I_k P] or [P I_k]	k-by-n
Parity-check	[-P`'` I_n-k] or [I_n-k -P`'` ]	(n-k)-by-n

where I_k is the identity matrix of size k and the ' symbol indicates matrix transpose. Two standard forms are listed for each type, because different authors use different conventions. For binary codes, the minus signs in the parity-check form listed above are irrelevant; that is, -1 = 1 in the binary field.

Examples

The commands below convert the parity-check matrix for a Hamming code into the corresponding generator matrix and back again.

parmat = hammgen(3)
genmat = gen2par(parmat)
parmat2 = gen2par(genmat) % Ans should be the same as parmat above

The output is

parmat =

     1     0     0     1     0     1     1
     0     1     0     1     1     1     0
     0     0     1     0     1     1     1

genmat =

     1     1     0     1     0     0     0
     0     1     1     0     1     0     0
     1     1     1     0     0     1     0
     1     0     1     0     0     0     1

parmat2 =

     1     0     0     1     0     1     1
     0     1     0     1     1     1     0
     0     0     1     0     1     1     1

gen2par - Convert between parity-check and generator matrices

Syntax

Description

Examples

See Also