modulation - Can we break the Shannon capacity?

I have a friend working in wireless communications research. He told me that we can transmit more than one symbol in a given slot using one frequency (of course we can decode them at the receiver).

The technique as he said uses a new modulation scheme. Therefore if one transmitting node transmits to one receiving node over a wireless channel and using one antenna at each node, the technique can transmit two symbols at one slot over one frequency.

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  I am not asking about this technique and I do not know whether it is correct or not but I want to know if one can do this or not? Is this even possible? Can the Shannon limit be broken? Can we prove the impossibility of such technique mathematically?

  
  


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  Other thing I want to know, if this technique is correct what are the consequences? For example what would such technique imply for the famous open problem of the interference channel?

  
  

Any suggestions please? Any reference is appreciated.

Answer

Most certainly not. While there has been some claims to break Shannon here and there, it usually turned out that the Shannon theorem was just applied in the wrong way. I've yet to see any such claim to actually prove true.

There are some methods known that allow for transmission of multiple data streams at the same time on the same frequency. The MIMO principle employs spatial diversity to achieve that. Comparing a MIMO transmission in a scenario that offers high diversity with the Shannon limit for a SISO transmission in an otherwise similar scenario might actually imply that the MIMO transmission breaks Shannon. Yet, when you write down the Shannon limit correctly for the MIMO transmission, you again see that it still holds.

Another technique to transmit on the same frequency at the same time in the same area would be CDMA (Code Division Multiple Access). Here, the individual signals are multiplied with a set of orthogonal codes so that they can be (perfectly in the ideal case) separated again at the receiver. But multiplying the signal with the orthogonal code will also spread its bandwidth. In the end, each signal employs much more bandwidth than it needs and I've never seen an example where the sum of the rates was higher than Shannon for the whole bandwidth.

While you can never be sure that breaking Shannon is actually impossible, it is a very fundamental law that stood the test of time for a long time. Anyone claiming to break Shannon has most likely made a mistake. There needs to be overwhelming proof for such a claim to be accepted.

On the other hand, transmitting two signals on the same frequency at the same time in the same area is easily possible using the correct method. This is by no means an implication that Shannon is broken.