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Subject: Re: Arithmetic coding of chess piece positions

Author: Peter McKenzie

Date: 11:28:58 11/15/99

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There is nothing magic about arithmetic coding, it only works well in
conjunction with a good model.

If you use arithmetic coding to encode an event that has a 50% probability, then
it will be encoded as exactly 1 bit just like huffman encoding.   Arithmetic
encoding only really excels when the model is asking it to encode events with a
very high probability (as predicted by the model).  In this case, it is possible
to effectively encode multiple high probability events into a single bit (the so
called 'splitting the bit').

A simple model for chess is to iterate over the 64 squares, encoding the
contents of each square.  You can build quite a sophisticated model that uses
chess specific knowledge to give probabilities for the contents of each square.
These probabilities would be adaptive, for example as soon as you 'see' a white
king and encode its square then you adjust the probabilities for the following
squares because they can't contain a white king.

Other models are possible, but in any case I doubt very much that you could
compress any given position into 64 bits.

cheers,
Petre



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