Analog fountain code (AFC) is a seamless rate adaptation strategy and was recently shown to closely approach the channel capacity without the channel state information at the transmitter side. The code was mainly designed for large block lengths and therefore the design for short packet communications which is one of the communication scenarios in 5G ultra-reliable and low latency communications (URLLC), is still not clear. We tackle this problem in this work and particularly focus on the design of the precoder which is shown to significantly affects the overall performance of the AFC in the short block length regime. We consider BCH codes as the precoder, and determine the rate of the code in order to maximize the realized rate under a given block error rate constraint. Simulation is performed to investigate the effect of choices for BCH precoder on the overall performance of BCH-AFC in terms of reliability and latency. We show that by selecting the appropriate BCH code as the AFC precoder, AFC performs closely to the normal approximation benchmark. We further proposed a threshold-based decoder to reduce the decoding complexity which is of significant importance in URLLC scenarios.

In this paper, we consider a massive grant-free non-orthogonal multiple access (GF-NOMA) scheme, where devices have strict latency requirements and no retransmission opportunities are available. Each device chooses a pilot sequence from a predetermined set as its signature and transmits its selected pilot and data simultaneously. A collision occurs when two or more devices choose the same pilot sequence. Existing GF-NOMA schemes assume that a collision of at least one pair of users entails a collision for all simultaneously transmitting users, which is sub-optimal in terms of individual outage and system throughput. For that, we propose a novel framework, where collisions are treated as interference to the remaining received signals. With the aid of Poisson point processes and ordered statistics, we derive simplified expressions that can well approximate the outage probability and throughput of the system for both successive joint decoding (SJD) and successive interference cancellation (SIC). Numerical results verify the accuracy of our analytical expressions. For low data rate transmissions, results show that the performance of SIC is close to that of SJD in terms of outage probability, for packet arrival rates up to 10 packets per slot. However, SJD can achieve almost double the throughput of SIC and is, thus, far more superior.

In this paper, we propose a multi-layer grant-free non-orthogonal multiple access scheme for short packet transmissions. In every time slot, users choose a layer randomly and independently of other users. Each layer corresponds to a code book, and users in each layer utilize the same code book and perform power control such that they have the same received power level at the Access Point (AP). Users of the same layer also choose the same pilot sequence that is transmitted with their code word, together with all users from other layers. The AP uses the pilot sequences to detect the layers selected and estimate the number of users in each layer. Using this information, the AP first separates the codewords corresponding to the different layers. Then, users of the same layer are decoded jointly. Based on this, we formulate an optimization problem to find the power levels that maximize the reliability of the system, i.e., the probability that an arbitrary user is decoded successfully, subject to some power and decoding complexity constraints. The problem is found to be non-linear and very complex. We propose some approximations that allow us to use mixed-integer linear programming (MILP). Numerical results show that the multi-layer setup can support a larger load with higher power efficiency for the same reliability and decoding complexity requirements.

Many uplink grant-free non-orthogonal multiple access (NOMA) schemes have been recently proposed to solve the massive access problem of M2M communications. However, little has been done on characterizing the performance bounds for such systems. In this paper, we take a step forward in this direction. We consider an uncoordinated NOMA scheme where devices have strict latencies and no retransmission opportunities are available. Devices choose pilot sequences from a predetermined set uniformly at random. Then, each device encodes its data using the pilot as the signature and transmits its selected pilot and data simultaneously with the rest of the devices. A collision occurs when two or more devices choose the same pilot sequence. Collisions are regarded as interference to the remaining set of transmitting devices. We first show that this interference can be well-approximated by a PPP. Then, we derive the average system throughput under joint decoding and massive access for a Rayleigh fading and path loss channel model. Our numerical results verify the accuracy of our derived analytical expressions. Finally, we investigate the impact of finite block lengths on the system throughput, i.e., when the decoding error probability is strictly non-zero. We show that we can support more than 10 packets per slot when the pilot sequences are large enough.

We propose a novel random access (RA) scheme with the quality of service (QoS) guarantees for machine-to-machine (M2M) communications. We consider a slotted uncoordinated data transmission period during which machine type communication (MTC) devices transmit over the same radio channel. Based on the latency requirements, MTC devices are divided into groups of different sizes, and the transmission frame is divided into sub-frames of different lengths. In each sub-frame, each group is assigned an access probability based on which an MTC device decides to transmit replicas of its packet or remain silent. The base station employs successive interference cancellation to recover all the superposed packets. We derive the closed-form expressions for the average probability of device resolution for each group, and we use these expressions to design the access probabilities. The accuracy of the expressions is validated through Monte Carlo simulations. We show that the designed access probabilities can guarantee the QoS requirements with high reliability and high energy efficiency. Finally, we show that RA can outperform standard coordinated access schemes as well as some of the recently proposed M2M access schemes for cellular networks.

In this paper, we analyze Luby Transform (LT) codes with unequal recovery time (URT-LT) and intermediate feedback. Different sets of information symbols within a message block are allocated different priorities, where the higher prioritized sets are to be recovered in a shorter time. We divide the encoding process into stages where in each stage different sets are allocated different selection probabilities. A stage ends when one of the sets' recovery times expires. We incorporate an intermediate feedback that notifies the transmitter of the recovered information symbols at the end of each stage. These recovered symbols are then excluded from future encoding. We use the AND-OR tree analysis to find the optimal selection probabilities that guarantee the sets are recovered within the required time, with a relatively small error probability. We compare the scheme to the case where the sets are encoded and transmitted separately.

In this paper, we investigate the impact of feedback in LT codes to guarantee unequal recovery time (URT) for different message segments. We analyze the URT-LT codes using the AND-OR tree for two scenarios: complete and partial feedback. We derive the necessary conditions for these two feedback schemes to achieve the required recovery time. We validate the analysis by simulation and highlight the cases where feedback is advantageous.

We revisit random multiple access (RMAC) for wireless systems with successive interference cancellation (SIC) employed at the access point (AP). We consider an asymptotically large number of users that transmit over a large number of orthogonal sub-channels. In each transmission block, each user chooses a degree d, where d is a random variable that follows a predefined degree distribution Ω(x). Then, users transmit in d sub-channels chosen uniformly at random. Specifically, we consider signal to interference and noise ratio (SINR) based RMAC where it is assumed that a user's information can be recovered successfully at a given iteration of the SIC process when its updated SINR is above a predetermined threshold. In this paper, we develop a generalized analytical framework based on the codes-on-graph representation to track the evolution of error probabilities in each iteration of the SIC process. We compare our approach to the conventional RMAC employing SIC which assumes that only clean, interference-free transmissions can be recovered successfully. This clean packet model relies on having time slots with a single user's transmission at each iteration of the SIC process. It was shown to be analogous to the iterative recovery process of codes-on-graph for the binary erasure channel (BEC), thus, allowing the direct application of the AND-OR tree analysis. We show that the clean packet model is a special case of our more generalized tree-based analytical framework. Our numerical results show that our model can support more users under the same power requirements.