bin2gray

(To be removed) Convert positive integers into corresponding Gray-encoded integers

bin2gray will be removed in a future release. Use the appropriate modulation object or function to remap constellation points instead. For more information, see Compatibility Considerations.

Syntax

y = bin2gray(x,modulation,M)

[y,map] = bin2gray(x,modulation,M)

Description

y = bin2gray(x,modulation,M) generates a Gray-encoded vector or matrix output y with the same dimensions as its input parameter x. x can be a scalar, vector, matrix, or 3-D array. modulation is the modulation type and must be 'qam', 'pam', 'fsk', 'dpsk', or 'psk'. M is the modulation order and must be an integer power of 2.

Note

If you are converting binary-coded data to Gray-coded data and modulating the result immediately afterwards, you should use the appropriate modulation object or function with the 'Gray' option, instead of bin2gray.

example

[y,map] = bin2gray(x,modulation,M) generates a Gray-encoded output y with its respective Gray-encoded constellation map, map.

You can use map output to label a Gray-encoded constellation. The map output gives the Gray-encoded labels for the corresponding modulation.

Examples

collapse all

Binary to Gray Symbol Mapping

Open Live Script

This example shows how to use the bin2gray and gray2bin functions to map integer inputs from a natural binary order symbol mapping to a Gray-coded signal constellation and vice versa, assuming 16-QAM modulation. In addition, a visual representation of the difference between Gray-coded and binary-coded symbol mappings is shown.

Convert Binary to Gray

Create a complete vector of 16-QAM integers.

M = 16;
x = (0:M-1);

Convert the input vector from a natural binary order to a Gray-encoded vector using bin2gray.

[y,mapy] = bin2gray(x,'qam',M);

Convert Gray to Binary

Convert the Gray-encoded symbols, y, back to a binary ordering using gray2bin.

z = gray2bin(y,'qam',M);

Verify that the original data, x, and the final output vector, z, are identical.

isequal(x,z)

ans = logical
   1

Show Symbol Mappings

To create a constellation plot showing the different symbol mappings, use the qammod function to find the complex symbol values.

sym = qammod(x,M);

Plot the constellation symbols and label them using the Gray (y) and binary (z) output vectors. The binary representation of the Gray-coded symbols is shown in black while the binary representation of the naturally ordered symbols is shown in red. Set the axes scaling so that all points are displayed.

scatterplot(sym,1,0,'b*');
for k = 1:16
    text(real(sym(k))-0.3,imag(sym(k))+0.3,...
        dec2base(mapy(k),2,4));
    
    text(real(sym(k))-0.3,imag(sym(k))-0.3,...
        dec2base(z(k),2,4),'Color',[1 0 0]);
end
axis([-4 4 -4 4])

Input Arguments

collapse all

`x` — Binary-encoded data
vector | matrix

Input binary-encoded data, specified as a vector or matrix.

Data Types: double

`modulation` — Modulation type
`'qam'` | `'pam'` | `'fsk'` | `'dpsk'` | `'psk'`

Modulation type, specified as, 'qam', 'pam', 'fsk', 'dpsk', or 'psk'

`M` — Modulation order
scalar

Modulation order, specified as an integer power of 2.

Data Types: double

Output Arguments

collapse all

`y` — Gray-encoded data
vector | matrix

Gray-encoded data with the same size and dimensions input x.

`map` — Map of labels
vector

Map output to label a Gray-encoded constellation, specified as a vector with a length the size of the modulation order, M. The map gives the Gray-encoded labels for the corresponding modulation.

Compatibility Considerations

expand all

`bin2gray` will be removed

Not recommended starting in R2020a

bin2gray will be removed in a future release. Use the appropriate modulation object or function instead. If your workflow uses bin2gray or gray2bin with any of the modulations schemes in this table, follow the appropriate example.

Modulation	Old Functionality	Use This Instead
QAM (`qammod` and `qamdemod`)	x = randi([0 63],1,100); y = bin2gray(x,'qam',64); z = qammod(y,64,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = qamdemod(x,64,'bin'); z = gray2bin(y,'qam',64);	x = randi([0 63],1,100); z = qammod(x,64,'gray'); x = 2(randn(100,1)+1jrandn(100,1)); z = qamdemod(x,64,'gray')
PAM (`pammod` and `pamdemod`)	x = randi([0 63],1,100); y = gray2bin(x,'pam',64); z = pammod(y,64,pi/4,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = pamdemod(x,64,pi/4,'bin'); z = bin2gray(y,'pam',64);	x = randi([0 63],1,100); z = pammod(x,64,pi/4,'gray'); x = 2(randn(100,1)+1jrandn(100,1)); z = pamdemod(x,64,pi/4,'gray')
FSK (`fskmod` and `fskdemod`)	x = randi([0 63],1,100); y = gray2bin(x,'fsk',64); z = fskmod(y,64,1,256,256,'cont','bin') x = 2(randn(512,1)+1jrandn(512,1)); y = fskdemod(x,64,1,256,256,'bin'); z = bin2gray(y,'fsk',64)	x = randi([0 63],1,100); z = fskmod(x,64,1,256,256,'cont','gray') x = 2(randn(512,1)+1jrandn(512,1)); z = fskdemod(x,64,1,256,256,'gray');
DPSK (`dpskmod` and `dpskdemod`)	x = randi([0 63],1,100); y = gray2bin(x,'dpsk',64); z = dpskmod(y,64,pi/4,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = dpskdemod(x,64,pi/4,'bin'); z = bin2gray(y,'dpsk',64);	x = randi([0 63],1,100); z = dpskmod(x,64,pi/4,'gray'); x=2(randn(100,1)+1jrandn(100,1)); z = dpskdemod(x,64,pi/4,'gray');
PSK (`pskmod` and `pskdemod`)	x=randi([0 63],1,100); y=gray2bin(x,'psk',64); z=pskmod(y,64,0,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = pskdemod(x,64,0,'bin'); z = bin2gray(y,'psk',64);	x=randi([0 63],1,100); z=pskmod(x,64,0,'gray'); x = 2(randn(100,1)+1jrandn(100,1)); z = pskdemod(x,64,0,'gray');

Modulation	Old Functionality	Use This Instead
QAM (`qammod` and `qamdemod`)	x = randi([0 63],1,100); y = bin2gray(x,'qam',64); z = qammod(y,64,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = qamdemod(x,64,'bin'); z = gray2bin(y,'qam',64);	x = randi([0 63],1,100); z = qammod(x,64,'gray'); x = 2(randn(100,1)+1jrandn(100,1)); z = qamdemod(x,64,'gray')
PAM (`pammod` and `pamdemod`)	x = randi([0 63],1,100); y = gray2bin(x,'pam',64); z = pammod(y,64,pi/4,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = pamdemod(x,64,pi/4,'bin'); z = bin2gray(y,'pam',64);	x = randi([0 63],1,100); z = pammod(x,64,pi/4,'gray'); x = 2(randn(100,1)+1jrandn(100,1)); z = pamdemod(x,64,pi/4,'gray')
FSK (`fskmod` and `fskdemod`)	x = randi([0 63],1,100); y = gray2bin(x,'fsk',64); z = fskmod(y,64,1,256,256,'cont','bin') x = 2(randn(512,1)+1jrandn(512,1)); y = fskdemod(x,64,1,256,256,'bin'); z = bin2gray(y,'fsk',64)	x = randi([0 63],1,100); z = fskmod(x,64,1,256,256,'cont','gray') x = 2(randn(512,1)+1jrandn(512,1)); z = fskdemod(x,64,1,256,256,'gray');
DPSK (`dpskmod` and `dpskdemod`)	x = randi([0 63],1,100); y = gray2bin(x,'dpsk',64); z = dpskmod(y,64,pi/4,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = dpskdemod(x,64,pi/4,'bin'); z = bin2gray(y,'dpsk',64);	x = randi([0 63],1,100); z = dpskmod(x,64,pi/4,'gray'); x=2(randn(100,1)+1jrandn(100,1)); z = dpskdemod(x,64,pi/4,'gray');
PSK (`pskmod` and `pskdemod`)	x=randi([0 63],1,100); y=gray2bin(x,'psk',64); z=pskmod(y,64,0,'bin'); x = 2(randn(100,1)+1jrandn(100,1)); y = pskdemod(x,64,0,'bin'); z = bin2gray(y,'psk',64);	x=randi([0 63],1,100); z=pskmod(x,64,0,'gray'); x = 2(randn(100,1)+1jrandn(100,1)); z = pskdemod(x,64,0,'gray');

Documentation

bin2gray

Syntax

Description

Examples

Binary to Gray Symbol Mapping

Input Arguments

`x` — Binary-encoded data
vector | matrix

`modulation` — Modulation type
`'qam'` | `'pam'` | `'fsk'` | `'dpsk'` | `'psk'`

`M` — Modulation order
scalar

Output Arguments

`y` — Gray-encoded data
vector | matrix

`map` — Map of labels
vector

Compatibility Considerations

`bin2gray` will be removed

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Topics

Communications Toolbox Documentation

Support

Documentation

bin2gray

Syntax

Description

Examples

Binary to Gray Symbol Mapping

Input Arguments

x — Binary-encoded data vector | matrix

modulation — Modulation type 'qam' | 'pam' | 'fsk' | 'dpsk' | 'psk'

M — Modulation order scalar

Output Arguments

y — Gray-encoded data vector | matrix

map — Map of labels vector

Compatibility Considerations

bin2gray will be removed

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Topics

Communications Toolbox Documentation

Support

`x` — Binary-encoded data
vector | matrix

`modulation` — Modulation type
`'qam'` | `'pam'` | `'fsk'` | `'dpsk'` | `'psk'`

`M` — Modulation order
scalar

`y` — Gray-encoded data
vector | matrix

`map` — Map of labels
vector

`bin2gray` will be removed

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.