decode

R2026b

Block decoder

Syntax

msg = decode(code,n,k)

msg = decode(code,n,k,codingMethod,prim_poly)

msg = decode(code,n,k,codingMethod,genmat)

msg = decode(code,n,k,codingMethod,genmat,trt)

msg = decode(code,n,k,codingMethod,genpoly)

msg = decode(code,n,k,codingMethod,genpoly,trt)

[msg,err,ccode,cerr] = decode(___)

Description

msg = decode(code,n,k) decodes the coded message code. The function assumes that the Hamming encoding method was used, with codeword length n and message length k.

msg = decode(code,n,k,codingMethod,prim_poly) decodes code assuming that prim_poly is the primitive polynomial used for encoding. This syntax applies when codingMethod is "hamming/binary" or "hamming/decimal".

msg = decode(code,n,k,codingMethod,genmat) decodes code assuming that genmat is the generator matrix used for encoding. This syntax applies when codingMethod is "linear/binary" or "linear/decimal".

msg = decode(code,n,k,codingMethod,genmat,trt) additionally specifies the decoding table trt. This syntax applies when codingMethod is "linear/binary" or "linear/decimal".

msg = decode(code,n,k,codingMethod,genpoly) decodes code assuming that genpoly is the generator polynomial used for encoding. This syntax applies when codingMethod is "cyclic/binary" or "cyclic/decimal".

msg = decode(code,n,k,codingMethod,genpoly,trt) additionally specifies the decoding table trt. This syntax applies when codingMethod is "cyclic/binary" or "cyclic/decimal".

[msg,err,ccode,cerr] = decode(___) additionally returns the message word errors err, the corrected codeword ccode, and the codeword errors cerr, using any input argument combination from the previous syntaxes.

Examples

Encode and Decode Message with Hamming Code

Set the values of the codeword length and message length.

n = 15; % Codeword length
k = 11; % Message length

Create a random binary message with the length equal to the message length.

data = randi([0 1],k,1);

Encode the message.

encData = encode(data,n,k,'hamming/binary');

Corrupt the encoded message by introducing an error at a random location.

errLoc = randerr(1,n);
encData = mod(encData + errLoc',2);

Decode the corrupted sequence. Observe that the decoder has correctly recovered the message.

decData = decode(encData,n,k,'hamming/binary');
numerr = biterr(data,decData)

numerr = 
0

Encode and Decode Message with Linear Block Code

Set the values of the codeword length and message length.

n = 7; % Codeword length
k = 3; % Message length

Create a random binary message with the length equal to the message length.

data = randi([0 1],k,1);

Create a cyclic generator polynomial. Then, create a parity-check matrix and convert it into a generator matrix.

pol = cyclpoly(n,k);
parmat = cyclgen(n,pol);
genmat = gen2par(parmat);

Encode the message sequence by using the generator matrix.

encData = encode(data,n,k,'linear/binary',genmat);

Corrupt the encoded message by introducing an error at a random location.

errLoc = randerr(1,n);
encData = mod(encData + errLoc',2);

Decode the corrupted sequence. Observe that the decoder has correctly recovered the message.

decData = decode(encData,n,k,'linear/binary',genmat);

Single-error patterns loaded in decoding table.  8 rows remaining.
2-error patterns loaded.  1 rows remaining.
3-error patterns loaded.  0 rows remaining.

numerr = biterr(data,decData)

numerr = 
0

Encode and Decode Message with Cyclic Block Code

Set the values of the codeword length and message length.

n = 15; % Codeword length
k = 5; % Message length

Create a random binary message with the length equal to the message length.

data = randi([0 1],k,1);

Create a generator polynomial for a cyclic code. Create a parity-check matrix by using the generator polynomial.

genpoly = cyclpoly(n,k);
parmat = cyclgen(n,genpoly);

Create a syndrome decoding table by using the parity-check matrix.

trt = syndtable(parmat);

Single-error patterns loaded in decoding table.  1008 rows remaining.
2-error patterns loaded.  918 rows remaining.
3-error patterns loaded.  648 rows remaining.
4-error patterns loaded.  243 rows remaining.
5-error patterns loaded.  0 rows remaining.

Encode the data by using the generator polynomial.

encData = encode(data,n,k,'cyclic/binary',genpoly);

Corrupt the encoded message by introducing three errors at random locations.

errLoc = randerr(1,n,3);
encData = mod(encData + errLoc',2);

Decode the corrupted sequence. Observe that the decoder has correctly recovered the message.

decData = decode(encData,n,k,'cyclic/binary',genpoly,trt);
numerr = biterr(data,decData)

numerr = 
0

Input Arguments

code — Input code

binary column or row vector | binary matrix with n columns | column or row vector of integers in the range [0, 2ⁿ – 1].

Input code, specified as one of these options:

• Binary column or row vector

• Binary matrix with n columns

• Column or row vector of integers in the range [0, 2ⁿ – 1]

Data Types: single | double

n — Codeword length

positive integer

Codeword length, specified as a positive integer such that n = 2^m – 1, where m is an integer greater than or equal to 2.

k — Message length

positive integer

Message length, specified as a positive integer such that k = n – m, where m is an integer greater than or equal to 2.

codingMethod — Error coding method and format

"hamming/binary" (default) | "hamming/decimal" | "linear/binary" | ...

Error coding method and format, specified as one of these options:

• "hamming/binary"

• "hamming/decimal"

• "linear/binary"

• "linear/decimal"

• "cyclic/binary"

• "cyclic/decimal"

Data Types: char | string

prim_poly — Primitive polynomial

gfprimdf(n-k) (default) | binary row vector | character vector | string scalar | positive integer

Primitive polynomial, specified as one of these options:

• Binary row vector — This vector gives coefficients of prim_poly in the order of ascending powers.

• Character vector or a string scalar — This value defines prim_poly in textual representation. For more information, see Representation of Polynomials in Communications Toolbox.

• Positive integer — This value defines prim_poly in the range [2^m + 1, 2^{m + 1} – 1].

For more information, see Default Primitive Polynomials and Primitive Polynomials and Element Representations.

Dependencies

This argument applies when you set CodingMethod to "hamming/binary" or "hamming/decimal".

Data Types: double | char | string

genmat — Generator matrix

k-by-n numeric matrix

Generator matrix, specified as a k-by-n numeric matrix.

Dependencies

This argument applies when you set CodingMethod to "linear/binary" or "linear/decimal".

Data Types: double

genpoly — Generator polynomial

cyclpoly(n-k) (default) | binary row vector | character vector | string scalar

Generator polynomial, specified as a polynomial character vector or a row vector that gives the coefficients in order of ascending powers of the binary generator polynomial. The value of genpoly for an [n, k] cyclic code must have degree n–k and divide xⁿ–1, where x is an identifier.

Dependencies

This argument applies when you set CodingMethod to "cyclic/binary" or "cyclic/decimal".

Data Types: double | char | string

trt — Decoding table

binary matrix

Decoding table, specified as a 2^n-k-by-n binary matrix. Create the decoding table using the syndtable function.

Dependencies

This argument applies when you set CodingMethod to "linear/binary", "linear/decimal", "cyclic/binary", or "cyclic/decimal".

Output Arguments

msg — Decoded messages

binary column or row vector | binary matrix with k columns | column or row vector of integers in the range [0, 2^k–1].

Decoded messages, returned as one of the options in the table. The value and dimension of msg depends on the value and dimension of code and the input message format.

code Value	Input Message Format	msg Value
binary column or row vector	binary	binary column or row vector
binary matrix with n columns	binary	binary matrix with k columns
column or row vector of integers in the range [0, 2n–1]	decimal	column or row vector of integers in the range [0, 2k–1]

Data Types: single | double

err — Message error correction information

column vector of integers

Message error correction information, returned as a column vector of integers. The length of the vector is equal to the number of message words. The vector entries can take these values:

• 0 — The function did not detect an error in the corresponding message word.

• 1 — The function detected and corrected an error in the corresponding message word.

• –1 — The decoding algorithm detected more errors in the corresponding message word than could be corrected.

ccode — Corrected code

binary column or row vector | binary matrix with n columns | column or row vector of integers in the range [0, 2ⁿ–1].

Corrected code, returned as one of these options:

• Binary column or row vector with n columns

• Binary matrix with n columns

• Column or row vector with n entries which are integers in the range [0, 2ⁿ–1]

The format of ccode matches that of code.

cerr — Codeword error correction information

column vector of integers

Codeword error correction information, returned as a column vector of integers. The length of the vector is equal to the number of message words. The meaning of this output depends on the format of code. If code is not a binary vector, cerr is equal to err. If code is a binary vector, this output contains error detection information for codewords. The information is given in the same way as in err.

More About

Default Primitive Polynomials

This table lists the default primitive polynomial used for each Galois field array GF(2^m). To use a different primitive polynomial, specify prim_poly as an input argument. prim_poly must be in the range [(2^m + 1), (2^m+1 – 1)] and must indicate an irreducible polynomial. For more information, see Primitive Polynomials and Element Representations.

Value of m	Default Primitive Polynomial	Integer Representation
1	D + 1	3
2	D2 + D + 1	7
3	D3 + D + 1	11
4	D4 + D + 1	19
5	D5 + D2 + 1	37
6	D6 + D + 1	67
7	D7 + D3 + 1	137
8	D8 + D4 + D3 + D2 + 1	285
9	D9 + D4 + 1	529
10	D10 + D3 + 1	1033
11	D11 + D2 + 1	2053
12	D12 + D6 + D4 + D + 1	4179
13	D13 + D4 + D3 + D + 1	8219
14	D14 + D10 + D6 + D + 1	17475
15	D15 + D + 1	32771
16	D16 + D12 + D3 + D + 1	69643

Algorithms

Depending on the decoding method, decode relies on lower-level functions such as hammgen, syndtable, and cyclgen.

Version History

Introduced before R2006a