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# Collision Resolution in Slotted ALOHA with Multi-User Physical-Layer Network Coding

Authors:
• Cohere Technologies

## Abstract and Figures

Two new schemes are proposed for collision resolu- tion in slotted ALOHA networks based on multi-user physical- layer network coding (MU PHY NC). In the proposed random access schemes, a collision of a generic number of packets can be recovered decoding the XOR of the original messages, such that the signal resulting from the collision is exploited rather than being discarded. Two different schemes that differ in terms of the amount of control information that needs to be transmitted from the access point, are studied.
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... Besides NCMA, recently there have been other efforts to apply network coding (including PNC) in multiple access networks. For example, [17]- [21] explored forming linear equations from the collided packets and derived source packets by solving the linear equations. However, [17], [18] only compute one equation for each overlapped packet, whereas NCMA can have more than one equation for each overlapped packet under favorable channel conditions. ...
... For example, [17]- [21] explored forming linear equations from the collided packets and derived source packets by solving the linear equations. However, [17], [18] only compute one equation for each overlapped packet, whereas NCMA can have more than one equation for each overlapped packet under favorable channel conditions. Furthermore, the decoding in [19]- [21] is based on PHY-layer equations only, while NCMA makes use of an outer MAC-layer channel coding scheme to achieve better utilization of the PHY-layer PNC packets. ...
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... In addition, the PNC technique can be adopted to multiple access networks [71,72,143]. A cross-layer scheme design is proposed to improve the throughput of wireless network in [71,72]. ...
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The thesis is dedicated to studying methods to improve the efficiency of random access schemes and to facilitate their deployment in machine-type communications (MTC). First, a joint user activity identification and channel estimation scheme is designed for grant-free random access systems. We propose a decentralized transmission control and design a compressed sensing (CS)-based user identification and channel estimation scheme. We analyze the packet delay and throughput of the proposed scheme. We also optimize the transmission control scheme to maximize the system throughput. Second, a random access scheme, i.e., the coded slotted ALOHA (CSA) scheme, is designed for erasure channels to improve the system throughput. By deriving the extrinsic information transfer (EXIT) functions and optimizing their convergence behavior, we design the code probability distributions for CSA schemes with repetition codes and maximum distance separable (MDS) codes to maximize the expected traffic load, under packet erasure and slot erasure channels. We derive the asymptotic throughput of CSA schemes over the erasure channels for an infinite frame length, which is verified to well approximate the throughput for a practical frame length. Third, an efficient data decoding algorithm for the CSA scheme is proposed to further improve the system efficiency. We present a low-complexity physical-layer network coding (PNC) method to obtain linear combinations of collided packets and design an enhanced message-level successive interference cancellation (SIC) algorithm to exploit the linear combinations of collided packets. We propose an analytical framework and derive the system throughput for the proposed scheme. The CSA scheme is further optimized to maximize the system throughput and energy efficiency.
... The k information packets of each user are then encoded into n h coded packets via its own chosen code c h . After encoding, a preamble P m and a pointer are attached to each of the n h coded packets, where the preamble is unique [25]- [28] and the pointer indicates the location of all other (n h − 1) coded packets for each user [12]. Moreover, each of n h coded packets is equipped with the information about the code chosen by the user. ...
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