gen2par

R2026b

Convert between parity-check and generator matrices

Syntax

H = gen2par(G)

G = gen2par(H)

Description

H = gen2par(G) converts a standard-form binary generator matrix to the corresponding parity-check matrix.

G = gen2par(H) converts a standard-form binary parity-check matrix to the corresponding generator matrix.

Examples

Convert Parity-Check Matrix for a Hamming Code to Generator Matrix

Convert the parity-check matrix for a Hamming code into the corresponding generator matrix and back again.

Create the parity-check matrix.

parmat = hammgen(3)

parmat = 3×7

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

Convert the parity-check matrix into the corresponding generator matrix.

genmat = gen2par(parmat)

genmat = 4×7

     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

Convert the generator matrix back again. The output, parmat2, should be the same as the original matrix, parmat.

parmat2 = gen2par(genmat)

parmat2 = 3×7

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

Input Arguments

G — Generator matrix

k-by-n matrix of binary values

Generator matrix, specified as a k-by-n matrix of binary values. The standard form of a generator matrix for a [n,k] binary linear block code is [I_k P] or [P I_k], where I_k is the identity matrix of size k.

Data Types: single | double

H — Parity-check matrix

(n-k)-by-n matrix of binary values

Parity-check matrix, specified as a (n-k)-by-n matrix of binary values. The standard form of a parity-check matrix for a [n,k] binary linear block code is [-P' I_n-k] or [I_n-k -P'], where I_n-k is the identity matrix of size (n-k).

Data Types: single | double

Output Arguments

H — Parity-check matrix

(n-k)-by-n matrix of binary values

Parity-check matrix, returned as a (n-k)-by-n matrix of binary values corresponding to the generator matrix G. The standard form of a parity-check matrix for a [n,k] binary linear block code is [P ' I_n-k] or [I_n-k -P '], where I_n-k is the identity matrix of size (n-k)

Data Types: single | double

G — Generator matrix

k-by-n matrix of binary values

Generator matrix, returned as a k-by-n matrix of binary values corresponding to the parity-check matrix H. The standard form of a generator matrix for a [n,k] binary linear block code is [I_k P] or [P I_k], where I_k is the identity matrix of size k.

Data Types: single | double

More About

Generator and Parity-Check matrices

Generator matrices and parity-check matrices are parameters that are required in order to process [n,k] generic linear block codes. For more information, see Configure Parameters for Linear Block Codes.

Version History

Introduced before R2006a