duo-binary signal coding SNR requirement

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neoflash

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snr requirement

Why duo-binary signal coding SNR requirement is 2.5dB more than normal binary coding?

According to my understanding, duo-binary coding will have 3 voltage level, binary code will only have two.

Thus the SNR ratio between them are 2/3, the difference should not be 2.5dB, it should be 3.5dB.

Any inputs?
 

2.5dB more transmit powre is needed for duobinary for having the same error probability as binary.

as Pe of duobinary and binary are known:

Pe(duobinary)=Pe(binary) ---> St(duobinary)~=1.8*St(binary) ---> St(duo,dB)~=2.5dB+St(binary,dB)

St is transmit power.
 

where is 1.8 coming from?
 

you know:

St(duo)/St(bin)=[(4*Q^-1(2*Pe/3)/pi)^2]/[(Q^-1(Pe))^2]

Q^-1(x) is inverse of Q(x) function,pi=3.14

calculating numerically (from table) :

for example : Pe=10^-3 then Q^-1(2/3*10^-3)=3.26 , Q^-1(10^-3)=3.09 you have (4*3.26/pi)^2/(3.09)^2~=1.8

for Pe=10^-4,... you will get about 1.8
 

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