# Spectrum Slicing for Multiple Access Channels with Heterogeneous Services
## 3 System Model
### Access Model  
We consider an uplink scenario with a set of users \(\mathcal{U}\) transmitting data to a Base Station (BS) over a single time-slotted multiple access channel. This single channel may consist of a single or of multiple subcarriers in an OFDMA system, whose number remains constant throughout the operation of the system. Users can transmit up to one packet per time slot, denoted by the index \(t\in\mathbb{Z}\), by occupying the available bandwidth and the entire duration of the slot. This can achieved by selecting a proper modulation and coding scheme based on the size of the payload to transmit. The study of multi-channel settings is considerably more complex, and left to future work, as having multiple concurrent resources in frequency domain changes the timing considerations significantly. There is as set of users \(\mathcal{U}\) in the system, composed of a single broadband user and multiple intermittent users. Specifically, user \(u_{B}\) is the broadband user following the eMBB model: it is a full-buffer user that always has data to transmit and maintains an infinite transmission queue. To counteract potential packet losses due to the noise, the broadband user implements a packet-level coding scheme, where blocks of \(K\) source packets are encoded to generate a frame of \(N\) coded packets of length \(\ell\) bits each. The basic operation of the broadband user is shown in Figure 1. The coded packets are linearly independent, which can be achieved, for example, with Maximum Distance Separable (MDS) codes or with Random Linear Network Coding (RLNC) with Galois-field size equal to \(\infty\). In effect, decoding any subset of \(K\) coded packets is sufficient for recovering the original block. The intermittent users belong to the subset \(\mathcal{U}_{l}=\mathcal{U}\setminus\{u_{B}\}\), where \(U_{l}=U-1\). They generate packets in each slot with a probability \(\alpha\) (i.e., they experience Bernoulli arrivals with parameter \(\alpha\)) and maintain a queue of up to \(Q\) generated packets. If a new packet is generated when the instantaneous length of the queue is \(Q\), these users discard the oldest buffered packet and add the newly generated one at the end of the queue. The choice of discarding the oldest packet in the queue follows a simple rationale: discarding any of the packets has the same effect on the overall reliability, choosing the oldest minimizes the latency for the ones that are delivered, as they will spend less time waiting for a slot in which they can be transmitted. In most practical cases, the queue will be set up so as to minimize the probability of discarding packets, but the case with short queues is relevant for low-power IoT devices with limited memory and computational resources. Packets are transmitted from the queue using First-In First-Out (FIFO) discipline, and the transmissions take place in the allocated slots. We consider a static allocation scheme, in which users are synchronized at the slot level. The set of users that are allocated slot \(t\) is denoted by \(\mathcal{A}_{t}\), where \(\mathcal{A}_{t}\subseteq\mathcal{U}\) s.t. \(\mathcal{A}_{t}\
eq\emptyset\). We define the following three types of slot allocations. 1. _Broadband:_ The slot is reserved for the broadband user. Hence, \(\mathcal{A}_{t}=\{u_{B}\}\). 2. _Intermittent:_ The intermittent users are allocated the slot and may use it if there are packets in their queues. Hence, \(\mathcal{A}_{t}\subseteq\mathcal{U}_{l}\). _Mixed:_ Both types of users are allowed to access the slot. Hence, \(\mathcal{A}_{t}\subseteq\mathcal{U}\) s.t. \(u_{B}\in\mathcal{A}_{t}\) and \(|\mathcal{A}_{t}|>1\). Next, we define the OMA and NOMA slicing based on the resource allocation as follows. 1. _OMA_: Slots can be either allocated to the broadband user or intermittent users; we define \(T_{\text{int}}\) to be the period between intermittent slots. 2. _NOMA_: Only mixed slots are allocated.