duo-binary signal coding SNR requirement

[neoflash]

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?

 

[mehtesham]

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.

 

[neoflash]

where is 1.8 coming from?

 

[mehtesham]

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