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# Maximum likelihood decoding of space time codes

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#### aregawi

##### Newbie level 2
Dear all,
I am currently doing my Master's thesis on 'coding and decoding of perfect space time block codes: analysis and performance simulation'.
The point is I wanted to reduce the complexity of ML decoding by conditional optimization principle that the order of complexity will reduce, for example,3x3 antenna dimension the constellation size the power of 6, which the order of 9 to transmit 9-HEX symbols.Can any one give me how i can estimate by ML, assuming that I transmitted 4-QAM symbols, after gray mapping symbowise or bitwise error probability. I want to implement it in matlab.I know the principle that after sending the symbols in a rayleigh fading channel,I will decode the one as correct pattern, let (x1,x2,x3,x4) out of all possible patterns of all these 4-symbols,which minimizes the error found by subtracting the code book of each pattern from what is received. But after finding the minimum error,how can I take the pattern out of it and compare it with the one the patterns at hand.I found it my approach as it has a drawback of accuracy and simplicity.
I will be happy if any one can give me a clue on this
(I needed i may send the exact problem)
Looking forward to receiving an earlier reply
with best regards,

Last edited:

if your looking towards using Matlab, then if you have the communication toolbox there is a function called vitdec, which will decode it. Which QAM are you talking about 8,16... The ML decoder uses a sliding window and gives the most reliable output.

If you look at the communication toolbox most of what you have mentioned already exists. Including modulation.

Childa909

### Childa909

Points: 2
Re: Maximum likelihood decoding of space time block codes

Dear Kalyanasv,
Lot of thanks for your earliest response of my problem.You recommended me to use a function vitdec(Viterbi Decoder) in the matlab toolbox, which suitable for Trellis codes. But here is the core of my question: my codes are space time block codes which are to be transmitted in the form of Alamouti blocks (the code being formed by cyclic arrangement of a certain pattern).
As they are in the form of independent blocks,it is possible to optimize of the the block elements with respect to the rest prior to maximizing the ML log function thereby that optimized value will be used to estimate the elements of the other blocks.Over all the order of complexity will be reduced than the conventional ML.I will use 9-HEX symbols for 3x3 antenna dimension and 16-QAM for 4x4. Here you the attache pdf :View attachment LOWCOMPLEXITY ESSENTIALLY MAXIMUM LIKELIHOOD DECODING OF PERFECT.pdf

I want to evaluate the performance of the conditionally optimized ML of 3x3 shown and do for 4x4 in the same way
With great thanks

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