Talk:Shannon's source coding theorem
I suggest the 'Shannon noiseless source coding theorem' article be merged with this 'Source coding' article.
--Hpalaiya 22:54, 19 May 2006 (UTC)
- this is a separate large article. maybe a summary of this article might be appropriate on the source coding page - strong disagree
Merge carried out, having first:
- renamed article from source coding to Shannon's source coding theorem
- redirected source coding to point to data compression
- moved material on variable length codes to variable length codes
- removed tag suggesting merger with entropy encoding
Some more clean-up to do, to blend the presentation of the two theorems more closely. (Detailed editing not yet started).
-- Jheald 22:00, 6 March 2007 (UTC).
I don't think that the that keeps showing up is ever explained/defined in this article. A quick explanation as to what it is would go a long way for someone that is not familiar with the material already.
An alternative proof for the symbol code case
Applying the Jensen's inequality for the expression we can have a direct proof without using any 's:
Using the Kraft's inequality on the right side:
Source coding theorem for symbol codes is wrong?
As far as I can see, Source coding theorem for symbol codes is wrong or at least is not accurate. Here is the counterexample: let , , , for other ( is the empty word), X is 0 or 1 with equal probability. Then, it is clear that f is decipherable code, but . There is also a counterexample that does not use the empty word. Could someone help to state this theorem more accurate? Alexei Kopylov (talk) 17:30, 5 May 2010 (UTC)
Well Alexei, Using any zero cost symbol (empty symbol), a message longer than a single symbol will not be uniquely decodable. It contradicits to the Kraft's inequality which is a necessary condition for decodability. Vamos (talk) 17:19, 12 May 2010 (UTC)
Oh, thanks! The problem was that the statement was about decipherable code, and there were no definition what decipherable code was. I changed it to uniquely decodable code, with the wiki link. See my change Alexei Kopylov (talk) 01:06, 14 May 2010 (UTC)
Why is no practical example included for the less mathematically inclined? I often find a practical example can greatly help to illustrate abstract concepts, and I think this would greatly enhance the usefulness of the article. — Preceding unsigned comment added by 18.104.22.168 (talk) 08:31, 27 June 2013 (UTC)