# Asynchronous Flipped Grant-Free SCMA for Satellite-Based Internet of Things Communication Networks
## 3 Asynchronous Flipped SCMA Scheme
### Codebook Collision Resolution in AF-SCMA  
SCMA is one of the most promising NOMA schemes, which allows different users to transmit the encoded codewords on the resource unit in an overlapping way. By designing the multidimensional constellation of SCMA codebook optimally, SCMA can obtain extra shaping gain, which makes SCMA achieve better performance in terms of BER [15]. To guarantee the excellent decoding performance, a codebook is allocated to a dedicated user by the central scheduler in one SCMA block in practice. However, in grant-free SCMA systems, each user chooses a codebook from the codebook set randomly, which makes it possible that two or more users choose the same codebook. If more than one user selects the same codebook and their packets are overlapped in the time domain, this leads to codebook collisions. Codebook collisions will destroy the shaping gain brought by the multidimensional constellations, which is destructive to packet-decoding.  
To alleviate the destructive impact of codebook collisions in asynchronous grant-free SCMA system, the proposed scheme exploits flipped diversity and SIC technique. Specifically, each MTD randomly selects two different codebooks from the codebook set to encode the data, and the original packet is transmitted with its flipped replica simultaneously. For packet-decoding, with the information of the small clear chunks (i.e., the chunks which are not interfered with by other chunks encoded with the same codebook) of a packet, the whole packet can be recovered, although the packet collides with other packets encoded with the same codebook.  
An example of codebook collision resolution is illustrated in Figure 2. In Figure 2a, three packets select the same codebook, and they interfere with each other. In this case, the shaping gain of multidimensional codewords vanishes, thus these three overlapping packets can hardly be decodedcorrectly. Figure 2b shows the procedure of decoding three interfered AF-SCMA packets which are also encoded with the same codebooks. \(A_{i}\), \(B_{i}\) and \(C_{i}\) represent the chunk number of packets A, B and C, respectively. The packets are encoded and transmitted with the concept of flipped diversity as mentioned above, and then SIC technique is adopted to recover the interfered packets. As shown in Figure 2b, \(C_{1}\) and \(C_{6}\) are a pair of clear chunks. Although they are overlapping in the time domain, encoding with different codebooks allows them still to be decoded correctly. Then the interference caused by \(C_{1}\) and \(C_{6}\) can be subtracted. Similarly, \(C_{2}\), \(C_{5}\) and \(C_{3}\), \(C_{4}\) are two pairs of clear chunks which can be decoded easily, and their replicas are subtracted to reveal more pairs of clear chunks. By removing the interference generated by chunks \(C_{3}\) and \(C_{4}\), a new pair of clear chunks \(A_{1}\) and \(A_{6}\) is revealed. The procedure of interference cancellation is executed in a zigzag pattern [31], and all these three packets can be decoded successfully.  
In AF-SCMA, we take advantage of shaping gain provided by different sparse codewords to construct a novel pair of packets (one is the original packet, the other one is its flipped replica). Although the flipped replica seems to bring extra interference to the original one, the performance of the SCMA decoder is still acceptable for moderate SNR. With the asynchronous nature of AF-SCMA, the arrived packets may only partially overlap with each other. Thus, we exploit the small clear chunks and the feature of chunk-bootstrap to recover the overlapping packets that are suffered from codebook collisions. Compared with other diversity transmission schemes, AF-SCMA transmits the packet and its flipped replica simultaneously, and no random intervals are needed between these two packets, which improves the transmission efficiency.