Viterbi decoding for QPSK,

[umardar27]

qpsk viterbi

Hi, can some one explain to me how the viterbi decoding is done for a qpsk system. I have not found any material on the net which explains the algorthym in detail for qpsk. ( i have understood the viterbi algorthym for bpsk). I shall be greatful if some one can help me in any regard and if possible can some one send me some matlab code for viterbi decoding with qpsk. I am really stuck , Thanks

 

[bulx]

qpsk viterbi coding

Assuming a rate 1/2 code, there is nothing special to do for QPSK. After BPSK demodulation you get one bit value (hard or soft, after one bit period). After QPSK demod you get values corresponding to both encoded bits (hard or soft, after one symbol period). . The viterbi algorithm need not be aware of the modulation scheme, it works as it does for BPSK.
-b

 

[umardar27]

viterbi decode soft

Thanks for the reply. But please bear with me and can you please help me a little bit more and explain in a little more detail how I have to implement QPSK.
In BPSK, we transmit + 1 ,whereas for QPSK we transmit + 1 + j ( four points ) How can you calculate the Euclidean distance from these points, we are taking soft decision criteria.
Let me explain my question a little bit more: lets say we transmitted [1 -1 -1 1 1] then after addition of noise we get at receiver [0.2 -0.9 0.1 0.9 1.8] we took these received values and found Euclidean distance between them and expected values from the trellis. Whereas in QPSK we transmit + 1 + j and the noise ( complex ) will make them alter. Now the expected values in BPSK were real values and how can we extract Euclidean distance from a complex value and a real value. Will the trellis for QPSK has to be changed or …
Please help me as deadline for my project is approaching and I am clueless what to do about it.
If any one has a MATLAB code written for the QPSK please do send me that as well for my understanding of the problem…
Thanking in advance
umardar

 

[bulx]

viterbi with qpsk input

Just consider bit pairs in QPSK, not individual bits as in BPSK

I pick the first pair from your example (0.2 -0.9)
Find the euclidean distance from all possible transmitted values ±1, ±1. Since each transition in the trellis corresponds to one of these 4 encoder output values, you can find the branch metrics.

Of course, there is the assumption that you know which the first and which is the second bit of each pair at the decoder, which is reasonable assumtpion for QPSK.

You cant do a straight decoding with an odd number of bits, but QPSK always produces bit pairs. Hope it is clear now.
-b

 

[umardar27]

viterbi decoding qpsk

Hi, Thanks once again. Things are getting clear. One more quiery is can we use the complex value for calculating the Euclidean distance or do we require to convert our complex values back to +-1 before getting into Viterbi decoding.
Thanking in advance
umardar

 

[bulx]

euclidian distance for viterbi

each branch metric is the euclidean distance of recieved point's (x,y) from the points ±1,±1. The distance is a 2D distance, with which you start viterbi decoding.
-b

 

[tzushky]

viterbi viterbi phase

I'm thinking of something else too: normally, you get an input waveform into the receiver, your demodulator does the job and you get phase information , since in QPSK the phase bears the bit information.... Isn't the phase euclidean distance (with the theortical phase of a symbol) that gives you the branch metrics in the VA?

I may be thinking more of uncoded QPSK...and even DQPSK too...