This is a technique performed during relaying. Say, for example, in a two way relay channel or bidirectional relay network the relay performs PLNC. This is given with XOR operation in mathematical expression. At relay, the electromagnetic interference of two nodes causes PLNC. This is what is given in research papers(IEEE Journals).
Pls substantiate the analogy. How does PLNC relate to XOR?
I do not think PLNC exactly corresponds to XOR, although the traditional network coding may correspond to XOR as the original symbol can be easily recovered by employing the property of XOR.
(A xor B) xor A = B and (A xor B) xor B = A
For PLNC as the name employs it occurs at physical layer and thus two signal from both sources naturally get mixed due to broadcast nature of wireless medium. The mixed symbol is then mapped to one of the known symbol combination conditioned on the fact that channel state can be perfectly estimated. The joint symbol is then transmitted according to some encoding scheme such as denoise-and-forward etc. I have seen some work on amplify and forward relaying too for PLNC but not sure how it works specifically. Will be really great if somebody has implemented PLNC in practice to notice its gains vs overhead of acquiring CSI etc.
The basic idea of PNC is to exploit the network coding operation that occurs naturally when electromagnetic (EM) waves are superimposed on one another and interfere naturally, this is called the PLNC. However, it is still possible to perform such XOR like operation at the relay if you could use if you could allocate the time slots for each transmission from the source. Then, if you have some channel coding, it can decode these symbols separately and then perform XOR operation (symbol-wise). If you do not assume any channel coding, then you can perform this in the soft domain (first detect the symbols separately using ML detector etc in each time slot. It has been a
common belief that PNC requires tight synchronization.
In fact XOR is only one possible function that PLNC may use, although it's the most obvious one for binary systems. Suppose two binary sources can each transmit a signal +1 or -1, and that these two signals are received by a relay exactly in phase and at the same amplitude, so that the signal values add. Then if both transmit +1, the received signal will be +2; if both transmit -1, it will be -2; and if one transmits +1 and the other -1 (either way round), it will be 0. This means that the relay cannot reliably decode either source. However it can decode the XOR function of the two - if the signal is +2 or -2, it returns 0 (because the two sources are the same); if 0, it returns 1 (because they are different), and this is the XOR of the binary symbols from the sources. The relay then broadcasts this to both terminals, which can use the approach Syed describes to determine the data transmitted from the other source.
In general the sources may not be binary (they could transmit QPSK or some higher order modulation), and the channels may not be in phase. In these cases some other function than XOR, probably a more complicated one, might be easier for the relay to decode - and if it is correctly chosen the terminals will still be able to regenerate the data they are interested in. So the function may not always be XOR.
As Syed mentions, you can use amplify and forward, where the relay just transmits the signal it receives. Then each terminals subtracts the interference due to its own transmission, and regenerates the signal sent by the other terminal.
In PLNC the mathematical operation that probably best describes it is just the "sum" in the complex plane. Furthermore, several authors actually use in their notation the "+" sign for PLNC and "⊕" for the Linear Network Coding.
there is another may be related term ANC analog netwrok Coding. what is the difference between ANC and PLNC. does PLNC is for digital signals?
if we suppose CSI is available then can we can get other terminal signal for two-way system in which both terminals signals get added with awgn noise at relay terminal we perform XOR and get other terminals signal with awgn in case of Amplify and forward. please correct
The PNC can be categorised into two basic sections; finite-field PNC and infinite-field PNC. In finite-field PNC, the target signal is represented by a finite field, for example, the XOR mapping (for binary bits) and the QPSK-5QAM mapping. In infinite-field PNC, the target signal is represented by an infinite field (e.g., a real number). Analog Network Coding (ANC) is an example of infinite-field PNC. Regardless of whether finite- or infinite-field PNC is adopted, the key requirement is that sources 1 and 2 (if two sources assumed) must be able to extract the information from the other end node from the mapped signal transmitted by relay.
As already mentioned by other researchers, in general, PNC mapping is not limited to just the XOR mapping. When it comes to ANC, the relay can perform a "summation" operation (e.g. a1+a2) and then simply amplifies and forwards. This inherits a huge disadvantage of noise amplification at the relay.
You may also like to read the following paper which explains the concept of ANC.
S. Katti, S. S. Gollakota, D. Katabi, “Embracing Wireless Interference: Analog network Coding,” ACM SIGCOMM ’07, pp. 397-408, Aug. 2007
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