Today, my colleagues asked me whether it is possible to achieve the
Shannon capacity when no coding is used. I answered to him as below,
then is it right?

Let channel be assumed only the BSC (binary symmetric channel), then
- If C = 1, yes it is possible since p = 0,
- Otherwise, we can not perfectly sure that not using coding
techniques, e.g. random codes or sequential mapping codes, makes
approach to the Shannon capacity.

where C is the Shannon capacity and p is the error probability.

Thanks in advance.
-- 
Best regards,
James K. (t...@hotmail.com)
- Any remarks, proposal and/or indicator to text would be greatly 
respected.
- Private opinions: These are not the opinions from my affiliation.
[HOME] http://home.naver.com/txdiversity

Hi James,

You're not wrong, but this statement is too weak:

> - Otherwise, we can not perfectly sure that not using coding
> techniques, e.g. random codes or sequential mapping codes, makes
> approach to the Shannon capacity.

Desiging a good coding system for a given channel is hard work -- it doesn't
happen by accident.  In general, you are always using some sort of channel
coding system when you transmit over the channel.  The rate at which you
transmit information, the amount of redundancy you introduce, and the types
of errors the system can recover from, are all designed based on assumed or
measured characteristics of the channel, in addition to any other
engineering constraints you may have.

James K. <t...@hotmail.com> wrote in message
news:<1...@4ax.com>...
> Today, my colleagues asked me whether it is possible to achieve the
> Shannon capacity when no coding is used. 

>  yes it is possible 

At the considerable risk of revealing my utter ignorance of 
communications theory -- isn't the presence of a coding scheme,
however trivial, a condition for achieving communications?

Suppose you monitor some channel. Unless you have access to a 
coding scheme (the "beeps" in a morse code are sufficient, 
in that they reveal the presence of a source, even if the morse
code itself would be unknown) you basically monitor random noise,
right?  Or did I miss something?

Rune

On Thu, 18 Dec 2003, Rune Allnor wrote:

> At the considerable risk of revealing my utter ignorance of
> communications theory -- isn't the presence of a coding scheme,
> however trivial, a condition for achieving communications?
>
> Suppose you monitor some channel. Unless you have access to a
> coding scheme (the "beeps" in a morse code are sufficient,
> in that they reveal the presence of a source, even if the morse
> code itself would be unknown) you basically monitor random noise,
> right?  Or did I miss something?
>
> Rune
>

rune, i agree with you.  a code is not necessarily a hamming code, or a
reed-solomon code, or an LDPC.  a code is simply a map from the set of
messages to the set of codewords that you can send to the channel.

of course, there is an abuse of terms when people talk about "uncoded
transmission" in the context of joint source-channel coding, such as toby
berger's famous example of white gaussian source and white gaussian noise
channel.  let the source be W_t and the transmitted signal be X_t.  then
the map X_t = \alpha W_t is optimal in the rate-distortion case, where
\alpha is chosen to meet the power constraint of your transmitter.

there are other examples, but that is for another discussion.

so i think the question is on how long the "memory" of the code is.  in
the case of binary symmetric channel with achievable rate < 1, there
exists a map from k message bits to n channel bits, k/n < C for which
transmission of information is arbitrarily reliable.  now, what about the
converse?  can one just use the same k bits in the channel and set the
rest to be 0?

julius

-- 
The most rigorous proofs will be shown by vigorous handwaving.
http://www.mit.edu/~kusuma

opinion of author is not necessarily of the institute

On Thu, 18 Dec 2003 06:15:44 -0500, Julius Kusuma <k...@mit.edu>
wrote:

>the map X_t = \alpha W_t is optimal in the rate-distortion case, where
>\alpha is chosen to meet the power constraint of your transmitter.

So, I think that the "uncoded but power constrainted" input can be
also optimal in the Gaussian input case since, in my idea, the
norm(power) of this input sequence when its elements goes infinity
becomes the constant say $\alpha^2$?

> now, what about the
>converse?  can one just use the same k bits in the channel and set the
>rest to be 0?

The power constraint meets the condition but the code space seems to
be smaller than the region of the optimal codes.

BR,
------
James K. (t...@hotmail.com)
- Any remarks, proposal and/or indicator would be greatly respected.
- Private opinions: These are not the opinions from my affiliation.
[Home] http://home.naver.com/txdiversity