Separation of Common and Unique Information

In the last post we were discussing about examples of common and unique information and were trying to explore its options in relay communication. Let us assume that the each relay node gets a part of the  codeword \(C\). The relay nodes if equipped to determine the common and the unique part of the information it received can use more power on the unique information part and a comparatively less power on the common information part.

For signals like images, the common and unique separation can be done using a multi-resolution filter. The low frequency(slowly varying) part forms the common information and the two orthogonal bandpass filters forms the unique information for the respective relay nodes. 

Suppose the source node performs a 2 slotted TDMA transmission, and half the relay nodes observes the first TDM symbol and the rest of the relay nodes observes the second TDM symbols what is the optimum coding that will result in achieving the decode-forward capacity? It is not very clear as to say in which domain does the separation exist. In the case of images though, we said it is the frequency domain.

Now once the separation domain becomes clear, the common information can be allotted some power level \(P_c\) and the unique part can be allotted some \(P_{u_1}\) and \(P_{u_2}\) respectively. If there exists two relay nodes then the power spent on the common part needs to be only \(\frac 12 P_c\). The other potential is that the common information can be transmitted when the channel gain is low, and an opportunistic communication can be performed for the unique information when the channel improves.

Common Informations Around Us

There is a good analogy for explaining common information. Consider the news of the Indian Cricket Team winning a test match. It does not really matter from which source you heard the news. This is because the PTI has handed over the news commonly to all the "newsmakers". Now consider news of the retirement of SRT. The decision (and of course the feelings associated) about his retirement is only known to him (and his close people) and different media reports in its unique way. The uniqueness in the reporting generates new information, and as a reader (viewer/listener) it is required to gather all these distinct pieces of information. 

SRT Retirement

 

Lords Test Win

The two news instances explains the term common information or shared information. 

Relating this to the relay communication scenario, we can observe that if the source is able to send unique information to each of the relay nodes, then the relay nodes can be used to its full efficiency. But this is a seemingly difficult task. Natural information comes as a combination of common information and certain unique information.

Information needs to be processed at the source to identify the common and unique information, and  then passed on to the relay. Each relay hence acts only as decode-forward nodes capable of only re-transmission of the information.