# A Filter-Based and Parallel Unknown Tag Identification Protocol in Open RFID Systems
## 4 Filter-Based and Parallel Unknown Tag Identification Protocol
### Collection Phase
#### 4.3.4 Collecting IDs in Parallel  
The reader broadcasts the request to issue the frame. Every \(m\) unknown tag sends its ID to the reader in the same slot. For an arbitrary unknown tag \(t_{ui}\), it adopts the following encoding scheme in place of _FM0_ and _Miller._: (i) The tag transmits the true code of \(V_{C}[u_{i}]\) in the \(\lceil\frac{h_{i}}{m}\rceil\)th slot if a bit of its ID is \"1\".  
(ii) The tag transmits the ones' complement code of \(V_{C}[u_{i}]\) in the \(\lceil\frac{h_{i}}{m}\rceil\)th slot if a bit of its ID is \"0\".  
Following the above rules, the number of real slots in the frame is \(\lceil\frac{h_{i}}{m}\rceil\). Considering the address code \"\(1010\)\" of \(t_{ui}\), the tag traverses each binary bit of its ID. In the ID, each \"0\" bit in the ID is encoded by \"\(0101\)\", and each \"\(1\)\" bit is encoded by \"\(1010\)\"; they are transmitted in the \(\lceil\frac{h_{i}}{m}\rceil\)th slot. Upon receiving the overlapping information, the reader isolates each ID of the tag by calculating normalized inner products of each \(m\) code and the address code of this tag. If the normalized inner product is \"1\", the bit received from this tag is \"1\"; if the normalized inner product is \"\(-1\)\", the bit received from this tag is \"0\"; otherwise, this tag did not send information.  
Take Figure 5 for example. The tags \(\{t_{u_{1}},t_{u_{3}},t_{u_{4}},t_{u_{6}}\}\) concurrently transmit their IDs in the \(1^{st}\) slot. The first two bits in the IDs of \(\{t_{u_{1}},t_{u_{3}},t_{u_{4}},t_{u_{6}}\}\) are \(\{10,11,10,00\}\). According to the rules (i) and (ii), the bits \"1\" and \"0\" are encoded by the true code and the one' -complement code of each tag's address code, respectively. Using \"1\" to represent \"0\" and \"+1\" to represent \"1\", \(t_{u_{1}}\) transmits \(\{(+1,+1,+1,+1),\)\((-1,-1,-1,-1)\}\), \(t_{u_{3}}\) transmits \(\{(+1,-1,+1,-1),\)\((+1,-1,+1,-1)\}\), \(t_{u_{4}}\) transmits \(\{(+1,+1,-1,-1),\)\((-1,-1,+1,+1)\}\), and \(t_{u_{6}}\) transmits \(\{(-1,+1,+1,-1),\)\((-1,+1,+1,-1)\}\) in the first slot. Therefore, the reader receives the final overlapping information \(\{(+2,+2,+2,-2),(-2,-2,+2,-2)\}\). The normalized inner product of the overlapping code and the address code determine whether a tag has sent data and what data to be sent. For example, the normalized inner product of \((+2,+2,+2,-2)\) and \((+1,+1,+1,+1)\) is \"1\", which indicates that the first bit \(t_{u_{1}}\) sent is \"1\"; the normalized inner product of \((-2,-2,+2,-2)\) and \((+1,+1,+1,+1)\) is  
Figure 4: Building real frame and address code vector in the collection phase.  
\"\(-1\)\", which indicates that the second bit \(t_{u_{1}}\) sent is \"0\". Consequently, the reader knows that the first two bits of \(t_{u_{1}}\)'s ID are \"10\". Similarly, the reader can obtain the IDs of the other three tags.  
If \(F_{R}[i]=0\), the unknown tags picking this slot will participate in the next round. Then, the collection phase will be executed for several rounds until the reader cannot detect replies from unknown tags in the channel.