Convert positive integers into corresponding Gray-encoded integers
y = bin2gray(x,modulation,M)
[y,map] = bin2gray(x,modulation,M)
y = bin2gray(x,modulation,M) generates a
Gray-encoded vector or matrix output
y with the same dimensions as
its input parameter
x can be a scalar, vector,
matrix, or 3-D array.
modulation is the modulation type and must be
M is the
modulation order that can be an integer power of 2.
[y,map] = bin2gray(x,modulation,M) generates a
y with its respective Gray-encoded constellation
You can use map output to label a Gray-encoded constellation. The map output gives the Gray encoded labels for the corresponding modulation. See the example below.
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.
This example shows how to use the
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 and binary coded symbol mappings is shown.
Create a complete vector of 16-QAM integers.
x = (0:15)';
Convert the input vector from a natural binary order to a Gray encoded vector using
[y,mapy] = bin2gray(x,'qam',16);
Convert the Gray encoded symbols,
y, back to a binary ordering using
z = gray2bin(y,'qam',16);
Verify that the original data,
x, and the final output vector,
z are identical.
ans = logical 1
To create a constellation plot showing the different symbol mappings, construct a 16-QAM modulator System object and use its associated
constellation function to find the complex symbol values.
hMod = comm.RectangularQAMModulator; symbols = constellation(hMod);
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 so that all points are displayed.
scatterplot(symbols,1,0,'b*'); for k = 1:16 text(real(symbols(k))-0.3,imag(symbols(k))+0.3,... dec2base(mapy(k),2,4)); text(real(symbols(k))-0.3,imag(symbols(k))-0.3,... dec2base(z(k),2,4),'Color',[1 0 0]); end axis([-4 4 -4 4])
Observe that only a single bit differs between adjacent constellation points when using Gray coding.