Calculation of the Exact Gain Offered by Gray over Binary Natural Code Mapping
T. Buzid
Journal of Information Technology Review, Vol. 4, No. 4, 2013.
DOI: 
Link: http://www.dline.info/jitr/fulltext/v4n4/2.pdf
Abstract:
The binary natural and the Gray binary reflected codes have been widely applied in many communication systems. In particular, Gray binary codes have been found to be optimum in reducing the error compared to binary natural codes. the Gray codes outperform the binary codes. In this paper the exact gain offered by Gray codes over binary codes is computed for the first time and found that the gain is dependent on the code-word length (constellation size), however at longer code-words the gain due to Gray labeling tends to remain at 3dB.