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The Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise (Wikipedia). This noise is specifically AWGN. Now, here is where my confusion lies. Isn't the purpose of error correction codes to remove the errors caused by AWGN + other causes of noise? Or is it every other type of noise except AWGN that we can correct with ERC. I understand that AWGN is completely random, or else we would have found a way to eliminate it. But my understanding is still hazy surrounding this.

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    \$\begingroup\$ Links and explanation of acronyms would be nice! \$\endgroup\$
    – Transistor
    Apr 12, 2016 at 22:39
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    \$\begingroup\$ The more noise you have, the more bits per second you have to waste on error correcting codes, and the less bits per second you have for useful data. \$\endgroup\$
    – user253751
    Apr 12, 2016 at 22:47

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Shannon's theory applies after all coding is applied. In other words, after the best possible coding / decoding system and unlimited latency, the resulting net data rate is the Shannon capacity.

You can compute capacities for different types of noise. The Gaussian channel (AWGN) is common example that is useful for practical communication systems.

See Cover and Thomas, Elements of Information Theory.

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  • \$\begingroup\$ Isn't that a kicker? My thesis guide was actually a student of Cover. Can you please expand on your first paragraph a little more? \$\endgroup\$
    – user91567
    Apr 13, 2016 at 3:23
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    \$\begingroup\$ The Shannon capacity is the maximum rate that data can be transferred with arbitrarily low error probability. Coding techniques are a way to achieve that probability. The Shannon limit just tells you the best you can possibly do with the best possible code. \$\endgroup\$ Apr 13, 2016 at 5:41
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You have to take into account, also, that the bits on Shannon theory are not the regular bits we transmit on communication channels. Bits on Shannon theory represent information. On a regular communication channel, not all bits transport information.

A string of 10 physical bits with the same value are equivalent to ONE Shannon bit of information.

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