Re: [Discuss-gnuradio] Re: gnuradio trellis

[Bob McGwier]

Achilleas Anastasopoulos wrote:

> Bob,
>
> Let's make sure we are talking about the same thing before
> we declare that we agree:
>
> Problem 1: KNOWN CHANNEL.
> In this case everything is quite straightforward, and all related
> problems have been solved 20 years ago.
>
> A) The receiver that minimizes SEQUENCE error probability is
> essentially a whitened matched filter followed by Viterbi.
>
> B) The receiver that minimizes SYMBOL error probability is
> a whitened matched filter followed by a MAP symbol detector;
> it is a bit more complicted than Viterbi (requires a forward and 
> backward recursion), but of similar nature
> (see the "trellis_siso_f" block in gr-trellis; that's what is doing!).
>
> ANY other algorithm (including EM) is indeed suboptimal.
>
> Problem 2: UNKNOWN channel.
> Here the situation is getting a bit more complicated as we
> have a problem of joint DETECTION and ESTIMATION.
> The optimal solution is exponentially complex in the sequence length, so
> it is of no practical interest. Over the last 15 years there have been
> several proposals in solving this problem.
> I won't go into that at all.
>
>
>
> Which problem are you referring to?
>
> From your reply I think you are referring to problem 1B.

I am indeed.

> I think you are proposing a suboptimal version of symbol detection 
> based on the EM algorithm. However, the optimal solution to this 
> problem is known as well, as I mentioned before, and is implemented in 
> gr-trellis
> in the block "trellis_siso_f".


This is great.   I did not know you had checked in the siso code in 
gr_trellis.  I am now more anxious to go study it more carefully.  I am 
glad I commented.


> Thus the statement "I personally believe that maximum likelihood 
> sequence estimation is suboptimal in comparison to a more completely 
> Bayesian approaching built upon computationally feasible 
> implementations of the EM algorithm" is wrong if it refers to problem 1A.
> If it refers to problem 1B then it unclear why one would want to
> implement the suboptimal EM if the optimal is known and available.
> Of course complexity/performance tradeoff will determine the solution
> to be implemeted in each practical scenario.
>
> Achilleas

Thanks for your rapid response!  I think we might find it useful to have 
such a suboptimal version as a variant.  I find it quite useful in many 
problems where the complexity is an issue and the performance of the 
suboptimal implementation is completely adequate.

Bob

--
Robert W. McGwier, Ph.D.
Center for Communications Research
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