How to Split Information ?

Splitting the information into non-overlapping chunks seems to be the problem ahead. Looking into the information as a vector space, we might ask if there exist a set of (non intersecting) subspaces that sums up to give the entire vector space (or the direct sum).

Showing that information is a vector space is not an easy task though. Depending on the class of information (for instance audio, text, image etc.) the vector space as well as the field over which it is defined changes. However a coding scheme can be associated with a vector space. 

Depending on the dimension of the code we are able to divide the space into sufficient number of subspaces that will depend upon the number of relay nodes as well. Information splitting hence becomes a code splitting or rate splitting problem.

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.