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Gray code to Binary conversion for PSK and PAM

Posted By Krishna Sankar On May 12, 2008 @ 5:47 am In Modulation | 18 Comments

Given that we have discussed Binary to Gray code conversion [1], let us discuss the Gray to BInary conversion.

Conversion from Gray code to natural Binary

Let be the equivalent Gray code for an bit binary number with representing the index of the bit.

1. For ,

i.e, the most significant bit (MSB) of the Gray code is same as the MSB of original binary number.

2. For ,

i.e, bit of the Binary number is the exclusive-OR (XOR) of of the bit of the Gray code and of the bit of the binary number.

Simulation model

Look Up Table based Matlab/Octave mode for Gray to Binary conversion

clear
% binary to gray code conversion
ipBin = [0:15] ; % decimal equivalent for a 4-bit binary
opGray = bitxor(ipBin,floor(ipBin/2))
% Gray to Binary conversion
[tt ind] = sort(opGray); % sorting Gray code elements to form the lookup table
opBin = ind(opGray+1)-1; % picking elements from the array

The Trick from DSP-Guru to do Gray to Binary [2] conversion [2], thanks to Jerry Avins [3].

clear
% binary to Gray code
ipBin = [0:15]
opGray = bitxor(ipBin,floor(ipBin/2))
% Gray code to binary
opBin = bitxor(opGray,floor(opGray/2^8)) ;
opBin = bitxor(opBin,floor(opBin/2^4)) ;
opBin = bitxor(opBin,floor(opBin/2^2)) ;
opBin = bitxor(opBin,floor(opBin/2^1)) ;

Concluding thoughts

1. As on now, I do not understand how the DSP Guru trick [2] for Gray code to Binary works. Of course, if I figure out, I will update this post. :)

2. Having discussed Binary to Gray code conversion and Gray to Binary conversion, we are now armed to discuss the bit-error rate probabilities for various modulation schemes (Recall: We have been discussing symbol error rate in Additive White Gaussian noise till date).

Thanks,
Krishna

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URL to article: http://www.dsplog.com/2008/05/12/gray-code-to-binary-conversion-for-psk-pam/

URLs in this post:

[1] Binary to Gray code conversion: http://www.dsplog.com/2008/05/11/binary-to-gray-code-conversion-psk-pam/

[2] DSP-Guru to do Gray to Binary: http://www.dspguru.com/comp.dsp/tricks/alg/grayconv.htm

[3] Jerry Avins: http://groups.google.co.in/group/comp.dsp/browse_thread/thread/081ff2279133b4c9#

[4] click here to SUBSCRIBE : http://www.feedburner.com/fb/a/emailverifySubmit?feedId=1348583&loc=en_US

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