Thursday 10 May 2012

LZ-77

LZ-77
I am not talking of a car model or something.
Its the dictionary based coding scheme in digital communications designed by lempel and ziv in 1977
They had an amazingly cool idea. The whole problem prior to this was that when we assume a source having certain distribution say Markov process but then  the source does not produce anything even near that particular process or does not produce states that agree with the general concepts of a Markov process.
Then the whole model goes for a toss. And sometimes instead of coding we end up with something that's even more sad as compared to the original source data stream.
So these guys said, Owell lets not assume what the source distribution instead lets build it up based on statistical model as when the source generates the output.
Hence, when an infinite sequence of source symbols have occurred and the source stabilises to some distribution without major changes, we have the statistics collected so far,  and then we can model based on those statistics itself generating one hell of a code.
The only problem is the fact that we are not assuming anything in the beginning. This is the source of one problem or another. In this case more specifically, we have no clue of the distribution till a lot of statistics have been collected. So, we transmit everything till that is available which kind of is clumsy
when the source changes its statistics or when we start something.
So, how can we overcome this problem??
Solutions may already exist which I am unaware of at this point.
But i feel why not just assume some model and code that way till we generate sufficient data
and then let the LZ algo kick in.
The model we chose might not be an exact representation but even if it does a decent job of coding
a lot is achieved in this bandwidth needy world.
I haven't quite thought of which models we can assume in the beginning.
More on that next time when i have some more idea of what we are exactly dealing with

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