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From: | Bob McGwier |
Subject: | Re: [Discuss-gnuradio] Re: gnuradio trellis |
Date: | Thu, 28 Sep 2006 16:27:17 -0400 |
User-agent: | Mozilla Thunderbird 1.0.8-1.4.1 (X11/20060420) |
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-trellisin 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 805 Bunn Drive Princeton, NJ 08540 (609)-924-4600 (sig required by employer)
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