in the case of the transmission without coding rate ( r=1/2)
I want to calculate the relationship between Ts (symbol time) as a function of Tb (bit duration) in modulation is DQPSK (Differential Quadrature Phase Shift Keying).,
QPSK/DQPSK is 2bits/symbol, so symbol time Ts = 2Tb; however in reality, note that "bit duration" is not really accurate here since both bits are sent simultaneously. It makes more sense to talk about bitrates, and DQPSK has double the bitrate compared to BPSK (which is 1bit/symbol), assuming the same symbol rate.
It makes sense define Ts as "symbol time" and Tb as "bit time" (not bit duration).
They are the inverses of symbol rate and bit rate respectively.
Regards
To get the effective bitrate for a given coding rate, you can just multiply it by the number of bits per symbol. So for QPSK/DQPSK we have 2 coded bits/symbol and 1/2 information bit/coded bit, giving 1 information bit/symbol, meaning Ts = Tb.