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The Shannon Limit (2010)

77 点作者 federicoponzi大约 4 年前

7 条评论

chrispeel大约 4 年前
Shannon&#x27;s original article &quot;A Mathematical Theory of Communication&quot; is available online, for example at [1]; I find it very readable. The MIT article talks about information theory as applied to our digital world, but does not mention that it&#x27;s now applied widely in theoretical physics; watch [2] for an intro. For example, the Hawking radiation from a black hole can function as an error correcting (erasure) code, allowing recovery of the information that fell into the black hole.<p>[1] <a href="http:&#x2F;&#x2F;people.math.harvard.edu&#x2F;~ctm&#x2F;home&#x2F;text&#x2F;others&#x2F;shannon&#x2F;entropy&#x2F;entropy.pdf" rel="nofollow">http:&#x2F;&#x2F;people.math.harvard.edu&#x2F;~ctm&#x2F;home&#x2F;text&#x2F;others&#x2F;shannon...</a><p>[2] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=v5UbN0xx4X0" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=v5UbN0xx4X0</a>
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bob1029大约 4 年前
Information theory is one of very few things out of academia that has really stuck with me and shaped how I look at problems in the world. The current applications for it are so vast and immediate that I wonder how many other places it could still be applied to.<p>Being able say and practice things like &quot;now let&#x27;s consider what this might look like in the frequency domain...&quot; can open up radical new approaches to solving problems. &quot;Ohhhh that signal&#x2F;channel has a hard roll-off starting at 20khz... I probably need to increase&#x2F;decrease my sample rate accordingly&quot; vs flying blind with traditional time domain analysis. In practical terms, frequency domain work is mandatory for things like high-efficiency video or audio codecs.<p>Understanding what entropy vs information really means is a huge part of being able to competently build cryptographic primitives from first principles.
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altcognito大约 4 年前
Previous discussion of the Shannon limit -- specifically the top end of analog lines:<p><a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=4344349" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=4344349</a>
dragontamer大约 4 年前
This MIT article is okay at an introduction to the subject.<p>I found the following Youtube video to be better however: <a href="https:&#x2F;&#x2F;simons.berkeley.edu&#x2F;events&#x2F;theoretically-speaking-mary-wootters" rel="nofollow">https:&#x2F;&#x2F;simons.berkeley.edu&#x2F;events&#x2F;theoretically-speaking-ma...</a><p>As a ~1-hour talk, Dr. Wootters is able to dig more deeply into Reed Solomon codes (a very popular error-correction code for nearly 50 years), as well as applications into strange stuff: like using RS codes in &quot;Test Pooling&quot; to save money on Syphilis tests (and probably the same methodology being used for &quot;Test Pooling&quot; in today&#x27;s COVID19 world).<p>Dr. Wootters keeps things relatively dumbed down, never getting too into the weeds of the math (and indeed: only sticks with the GF(5) field, a prime field instead of talking about the more applicable extension fields). Still, extension fields follow mostly the same concepts, and GF(5) is sufficient to cover all the concepts.
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jzer0cool大约 4 年前
So what was the code that was finally sought after and developed mentioned at the very end of the article?
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teekert大约 4 年前
So how does this relate to Hamming codes? [0]<p>[0] <a href="https:&#x2F;&#x2F;m.youtube.com&#x2F;watch?v=X8jsijhllIA" rel="nofollow">https:&#x2F;&#x2F;m.youtube.com&#x2F;watch?v=X8jsijhllIA</a>
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touisteur大约 4 年前
Right when I was trying to understand compressed sensing, amazing stuff...