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Author Topic: Truly understanding trellis coded modulation  (Read 642 times)

Weaver

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Truly understanding trellis coded modulation
« on: May 17, 2018, 06:21:55 PM »

If I try to explain trellis coded modulation then someone can tell me whether I have complete misunderstood it, got part or all of it wrong, am missing whole vital pieces of the story. Would someone help with that?

It seems to me that trellis coded modulation should not be just shortened to trellis coding as it is not just another code, that's the whole point of why it is so revolutionary. When Ungerböck invented it in the 1970s it was the first time that anyone had blurred the boundary between coding and modulation (=choosing waveforms) so that the two can't be dealt with solely in isolation but have to be cionsidered together and a design was produced that links the two, with a coding scheme that only makes any sense if a particular associated type of modulation is also used with that coding; the two were co-designed, and have to be.

You have a QAM constellation with so many points in it. One of those points on a 2d plane is the value of a transmitted symbol and as it is 2d its position can be written as a pair of numbers (x,y) coordinates or viewed as a complex number x + iy. The distance d between two points is the euclidean distance given by pythagoras as d² = x² + y² . The euclidean distance is a measure of how distinct the values are, of who difficult it is to confuse two symbols and decide you're hearing one value when another value was intended. If the distance is too small then the points will be too easily confused in the presence of noise.

The trellis idea is that you take the set of all possible positions of a point in the constellation and you split or ‘partition’ that set into so many distinct subsets of possible points, say into two subsets that are halves, or four quarters or whatever. The magic of trellis comes in when it was realised that if you pick the subsets intelligently you can do it in such a way that the points in a subset partition are all spaced apart much further in fact spaced so that the minimum distance between any point in one subset and any of the neighbours that belong to the other subsets is really large compared to the nearest distance spacing found in the full whole subset. Keeping points much further apart like this hugely increases noise resistance because it is much more difficult to get points confused.

The coding part of TCM is where values of symbols were restricted so that they were limited by having to conform to a time sequence of permitted values, symbols could not be sent in completely random patterns the value of one symbol was restricted depending on the previous so many symbols sent, so only certain sequences in time were legal. A signal corrupted by noise can be spotted as corrupt because the received pattern does not conform to any of the allowed pattern sequences. The restrictions on permitted sequences of values form a code, and this restriction means fewer possible combinations of symbols over time, so it slows communication down. However, by some surprising miracle, it turns out that the extra noise immunity gained by the modulation scheme that uses set partitioning can be used to give a performance benefit that is greater than the performance loss due to the long-windedness imposed by the trellis code requiring the generation of more bits as output from the code to send a given message. The extra noise immunity can either be kept as a reliability benefit or the system can be pushed harder to get more speed by having a more complex and thus more fragile / risky constellation with more points in it with the more robust modulation scheme restoring reliability to the same level. So it really is a free lunch. It is very surprising that this is true. Surprising that a coding scheme that makes transmitted data more long-winded can actually end up speeding the whole thing up.

The cost is in the complex decoding process which involves looking at the time pattern of the received sequence of symbols and comparing it to the permitted time sequences to try and guess which was the most likely intended transmitted value. There is quite a lot of information available here in the possibly slightly corrupted or more corrupted information coming in and different decoding algorithms can cost more cpu cycles or more silicon.

I hope that some of that is correct. Would someone tell me what is wrong / right, if anything?
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kitz

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Re: Truly understanding trellis coded modulation
« Reply #1 on: May 17, 2018, 08:20:08 PM »

This is my take on it, from back in the days when I could get my head around things and pre-pain, FM and Gabapentin blurring my headspace.
TBH I don't intend re-capping it atm as GDPR is taking up all my energy right now.

I wrote this when there wasn't hardly anything about TCM elsewhere on the net and I could still code compression type algorithms so it may have a programmers edge on it, but I tried to explain it in a two dimensional way to aid understanding.

https://kitz.co.uk/adsl/error_correction.htm#Trellis
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Weaver

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Re: Truly understanding trellis coded modulation
« Reply #2 on: May 27, 2018, 06:23:14 PM »

Could anyone tell me if they think I got it right, or got it wrong, or made a hash of the above?
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CarlT

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Re: Truly understanding trellis coded modulation
« Reply #3 on: May 27, 2018, 07:56:33 PM »

I really hope I retain your level of intellectual curiosity when I am retired, Sir.  :fingers:
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Weaver

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Re: Truly understanding trellis coded modulation
« Reply #4 on: May 27, 2018, 09:25:41 PM »

I am retired due to ill-health, not extreme age. But it amounts to the same thing. Crap brain. Found some excellent lectures on quantum field theory on youtube - google tobias osborne. The web and youtube, god I wish I had had things such as this when I was in my teens, things would have been so different.
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spring

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Re: Truly understanding trellis coded modulation
« Reply #5 on: May 28, 2018, 12:42:49 PM »

I am retired due to ill-health, not extreme age. But it amounts to the same thing. Crap brain. Found some excellent lectures on quantum field theory on youtube - google tobias osborne. The web and youtube, god I wish I had had things such as this when I was in my teens, things would have been so different.
I lost so much of my brain 2 years ago that I have about half the amount of cells left in the frontal lobe if not the whole brain, and have tardive akathisia and my body similar to that of a parkinsonian especially as time goes by. 32mg Perphenazine could have ended up in my body only because of Psychiatry creating it and killing with it. 16 is enough to do the same but not in a mere 6 weeks. What I was given is 16 but with Sertraline 100mg that increases the blood levels to 32, because it was given 2 months prior to starting Perphenazine and it took a month to get to 16, leading to acute intoxication. All of this on purpose. This actually happend after being hospitalized for 0 reason on purpose, to be injected Haloperidol and be made a complete zombie, I got out without those shots, just yet another blood-level increasing combination of Fluoxetine 20mg+Haloperidol 2mg that increased it to 20-30mg, but then stopped it as soon as I got out with things getting better every day, damaged but alive. I always wanted to steer clear of Psychiatry but the situation got there just like that and totalled 2 hospitalizations over 3 years, then I got killed on private counseling by being fooled into taking Perphenazine 16mg that is in the end 32mg to replace something else that wasn't ideal to continue taking (the strongest anti dopamineric approved for prescription by the FDA, 5 times stronger than Haloperidol, and also affects an additional receptor type. Each time it attaches to a doapmine receptor it sets it back to 14% activity, on a total of two receptor types) instead of being put on the weakest medication (for it to be easier to stop eventually), when it damages you at any amount, 4mg Perphenazine is enough in at least two thirds of the cases that Perphenazine is their last resort, because it instantly starts killing you with the speed determined by the dose. It spell binds you once you take it too and you are incapable of comprehending key elements in the situation. I've just been dragged into it, doesn't matter how anymore. I blame my family for this, because I only wanted to distance myself as far as possible from it and never have I wanted to take any of it because I knew it is pure poison, and everyone is totally fine when it's not them taking it, pushing others into it. I was forced to go or have to take being terrorised as if I'm making some grave error. People take what seems like an eternity to remove their wishful thoughts about the existence of Psychiatry. I didn't even want to private counsel, nor did I trust any psychiatrist, but pressure from people affects other people all the time. I can't feel any emotions anymore, they just start and are fully inhibited. And my brain hurts the last two years without a moment of halt, in a nearly unbearable amount, but in my spirit I can't bear it anymore.

Hope it wasn't too long.
« Last Edit: May 28, 2018, 02:12:17 PM by spring »
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Weaver

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Re: Truly understanding trellis coded modulation
« Reply #6 on: May 28, 2018, 12:43:46 PM »

Sorry to hear that!
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johnson

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Re: Truly understanding trellis coded modulation
« Reply #7 on: May 28, 2018, 03:17:28 PM »

And my brain hurts the last two years without a moment of halt, in a nearly unbearable amount, but in my spirit I can't bear it anymore.
Hope it wasn't too long.

Hang in there my friend. Brains are remarkable things that can reorganise themselves and self heal in ways that seem impossible.
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