Gray code to Binary conversion for PSK and PAM
Given that we have discussed Binary to Gray code conversion, 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.
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Binary to Gray code conversion for PSK and PAM
In this post, let us try to understand Gray codes and their usage in digital communication. Quoting from Wiki entry on Gray code [Gray-Wiki],
The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one digit.
In a digital communication system, if the constellation symbols are Gray encoded, then the bit pattern representing the adjacent constellation symbols differ by only one bit. We will show in another post that having this encoding structure gives a lesser probability of error than the ‘natural binary ordering’. However, in this post, let us try to figure out the conversion of natural binary representation to Gray code.
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OT: Migration to a Deep Blue template
After almost 6 months with the Smashing Theme template, its time for a change. Recently I stumbled upon the Deep Blue template from DailyBlogTips. I liked the clean blue-green-white combination and and felt it might be a good fit for www.dsplog.com. Hope you agree.
One key feature which I like is addition of tag cloud in the sidebar. Hopefully navigating to the relevant posts became simpler. Have a look around.
Of course, your valuable comments and criticism are welcome. 
Eye diagram with raised cosine filtering
We have discussed about probable transmit pulse shaping filter and have observed that raised cosine filtering filtering allows a simpler implementation, albeit at the cost of increased bandwidth. Let us know understand the eye diagram, which is a useful graphical tool to quantify the degradation of the signal due to filtering.
Eye diagram
An eye diagram is generated in an oscilloscope operating in the persistence mode by observing the output of the filter with the symbol timing serving as the trigger. The observation window can be set as 2 times the symbol period. (Refer. Section 5.1.3 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]).
MCDES 2008 at Indian Institute of Science, Bangalore
Thanks to Prof. K V S Hari, I was informed that the centenary year for Indian Institute of Science (IISc), Bangalore starts on May 27th 2008.
As part of the event, a conference with the theme Managing Complexity in a Distributed World (MCDES) is to be held at IISc from May27th to 31st 2008.
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