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 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 bin2gray.
y = bin2gray(x,'qam',16);
Convert the Gray encoded symbols, y, back to a binary ordering using gray2bin.
z = gray2bin(y,'qam',16);
Verify that the original data, x, and the final output vector, z are identical.
isequal(x,z)
ans =
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(y(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.