Physical-layer Network Coding Aided Polar Slotted Random Access Algorithm

SHAO Caiping; QIU Yuping; XIE Zhaopeng; SONG Dan; CHEN Jian; CHEN Pingping

doi:10.11999/JEIT260867

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SHAO Caiping, QIU Yuping, XIE Zhaopeng, SONG Dan, CHEN Jian, CHEN Pingping. Physical-layer Network Coding Aided Polar Slotted Random Access Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260867

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SHAO Caiping, QIU Yuping, XIE Zhaopeng, SONG Dan, CHEN Jian, CHEN Pingping. Physical-layer Network Coding Aided Polar Slotted Random Access Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260867

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Physical-layer Network Coding Aided Polar Slotted Random Access Algorithm

doi: 10.11999/JEIT260867 cstr: 32379.14.JEIT260867

1.
College of Advanced Manufacturing, Fuzhou University, Quanzhou 362251, China
2.
College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China
3.
Navigation College, Jimei University, Xiamen 361021, China

Funds: The National Natural Science Foundation of China(62571134), The Young Scientists Fund of the National Natural Science Foundation of China (62501252), Fujian Provincial Industry-University-Research Cooperation Project (No.2024H6013)

Accepted Date: 2026-08-26
Rev Recd Date: 2026-08-26

Available Online: 2026-09-01

Abstract

Abstract

Objective Massive Machine-Type Communications (mMTC) constitutes a fundamental pillar of 5G and emerging 6G wireless networks, dedicated to supporting massive connectivity for the Internet of Things (IoT). In grant-free random access scenarios, sporadic and uncoordinated transmissions by massive terminals inevitably induce severe packet collisions under heavy traffic loads. Traditional scheduled access protocols become inefficient due to prohibitive signaling overhead. Consequently, grant-free slotted ALOHA protocols based on Successive Interference Cancellation (SIC)—such as Contention Resolution Diversity Slotted ALOHA (CRDSA), Irregular Repetition Slotted ALOHA (IRSA), and Coded Slotted ALOHA (CSA)—have garnered widespread attention. However, these classical schemes fundamentally rely on the presence of collision-free (degree-1) slots to trigger and sustain the iterative graph-peeling decoding process. Under practical constraints of finite frame lengths and heavy traffic, collision-free slots are drastically depleted, causing severe decoding stalling and throughput degradation. Furthermore, pure SIC mechanisms are intrinsically vulnerable to error propagation. Although Polar Slotted ALOHA (PSA) introduces polarization transforms across time slots to enhance packet recovery, its collision resolution remains constrained by the initial SIC condition. To resolve these challenges, a joint decoding algorithm combining Polar Slotted ALOHA with Physical-Layer Network Coding (PSA-PNC) is proposed over the Slot Erasure Channel (SEC). The objective is to transform destructive multi-user packet collisions into algebraically solvable linear network coding equations, thereby eliminating the strict reliance on collision-free slots and significantly elevating concurrent multi-user detection capability and throughput performance under heavy traffic loads. Methods A joint physical-layer and MAC-layer random access framework is established over the Slot Erasure Channel (Fig. 1). At the transmitter side, active users independently select transmission time slots based on an irregular degree distribution polynomial without inter-user coordination or channel collision feedback. The sender remains blind to multi-user collision patterns in the channel. At the base station receiver, the superimposed signals across slots are equivalently modeled as a sparse global input matrix over a binary finite field, followed by packet-level polar encoding. To resolve dense collisions without relying on clean slots, a closed-loop iterative receiver architecture is developed (Fig. 2). In each iteration, channel observation sequences are initially processed by a packet-level Successive Cancellation (pSC) or packet-level Successive Cancellation List (pSCL) decoder to extract reliable equivalent combined packets from information slots. Instead of being discarded, the collided slots corresponding to these reliable packets are utilized to construct a local sparse linear Network Coding (NC) equation system. A Generalized Matrix Inversion (GMI) criterion is subsequently executed to analyze the column-rank characteristics of the access pattern matrix and achieve global algebraic multi-user decoupling. Solvable user packets are directly recovered without requiring full-rank matrix conditions or degree-1 slots. The algebraically decoupled user packets are then utilized as prior information to reconstruct physical-layer codewords and subtracted from the observation buffer via iterative SIC, continuously reducing the dimensionality of the unresolved collision space. High-reliability packets output by the pSCL decoding paths are leveraged in the iterative loop to effectively suppress error propagation and guarantee the linear independence of residual equations. Furthermore, the polarization evolution process of equivalent multi-user packets over the SEC is theoretically proved to be equivalent to that over a scalar Binary Erasure Channel (BEC), enabling rigorous calculation of frame error rate bounds via Bhattacharyya parameters (Fig. 3). Results and Discussions Extensive theoretical analyses and Monte Carlo simulations are conducted to evaluate the performance of the proposed PSA-PNC scheme over the Slot Erasure Channel. The theoretical polarization bounds of packet-level polar decoding are verified under various slot erasure probabilities ($ \epsilon \in \left\{0.1,0.2,0.3\right\} $), exhibiting precise consistency with simulation curves and validating the polarization threshold effect (Fig. 3). In terms of system throughput, simulation results demonstrate that for a frame length of $ N=1024 $, the proposed PSA-PNC scheme with pSCL ($ L=8 $) achieves a peak normalized throughput of approximately 0.87 packets/slot at a normalized load of $ G\approx 0.90 $, yielding an approximate 15% throughput improvement over baseline PSA and outperforming Coded Slotted ALOHA under identical finite-length configurations (Fig. 4(a)). In the low-load region, all evaluated schemes exhibit near-identical linear throughput growth due to the abundance of collision-free slots (Fig. 4(a)). When the slot erasure rate increases to $ \epsilon =0.35 $, the number of recoverable reliable equivalent packets decreases, leading to insufficient NC equations and observable throughput degradation in high-load regions, which confirms the operational boundary of the algorithm (Fig. 4(a)). For a short frame length of $ N=64 $, a consistent throughput gain ranging from 0.12 to 0.18 is maintained by PSA-PNC, demonstrating strong robustness against finite-length decoding stalling in short-packet scenarios (Fig. 4(b)). In terms of transmission reliability, under a target Packet Loss Rate (PLR) of $ {10}^{-2} $ at $ N=1024 $, the supportable normalized load upper bound is extended from $ G\approx 0.75 $ in baseline PSA to $ G\approx 0.84 $ in PSA-PNC (Fig. 5(a)). Furthermore, steeper waterfall regions and significantly lower error floors are consistently maintained across various frame lengths from $ N=64 $ to $ N=1024 $ (Fig. 5(b)). Conclusions A joint decoding scheme combining Polar Slotted ALOHA with Physical-Layer Network Coding (PSA-PNC) is established to resolve the severe decoding stalling problem in grant-free random access. By constructing a closed-loop iterative receiver integrating packet-level polar decoding, GMI-based algebraic equation solving, and iterative SIC cancellation, destructive multi-user collisions are converted into solvable linear equations. The dependence on collision-free slots is effectively eliminated, and the supportable load threshold, peak normalized throughput, and packet recovery reliability are substantially enhanced under heavy traffic loads. Future research will be directed toward non-ideal multipath fading channels, such as Rayleigh fading, and the design of low-complexity sparse receiver architectures for practical massive access implementations.
- Random Access(RA),
- Polar code,
- Collision resolution,
- Multi-user detection,
- Network Coding(NC)

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References(25)

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