本文提出了一種卷積編碼波以松接收器(Convolutional Coded Poisson Receivers, CCPRs)的框架，將空間耦合技術融入到波以松接收器的結構中。我們引入機率密度演化(density evolution)方程式，使用連續干擾消除(Successive Interference Cancellation, SIC)演算法追蹤封包解碼過程。此外，在通訊通道在可以使用阿羅哈接收器建模時，我們推導出穩定區域（編碼波以松接收器和卷積編碼波以松接收器均能以機率1成功接收每個封包的區域）之上界。同時，我們還利用位能理論專門分析了單一類別用戶的情形下穩定區域的上界。此上界推廣了空間耦合不規則重複時槽阿羅哈 (Irregular Repetition Slotted ALOHA, IRSA)協議的上界，且只要這些模型可以表示為波以松接收器，則同樣適用於具有多個流量類別的通訊通道模型。此外，我們通過位能理論確定了構建卷積編碼波以松接收器的窗口大小條件，以確保相對於傳統卷積編碼波以松接收器具有更大的滲透閾值(percolation threshold)。對於多類別接收器與多類別使用者的情型，我們遞歸地計算機率密度演化方程式，以確定穩定區域的邊界。數值結果表明，通過利用空間耦合方法，相較於編碼波以松接收器，卷積編碼波以松接收器的穩定區域可能會擴大。

In this paper, we present a framework for convolutional coded Poisson receivers (CCPRs) that incorporates spatial coupling into the architecture of coded Poisson receivers (CPRs). We use density evolution equations to track the packet decoding process with the successive interference cancellation (SIC) technique. When the underlying channel can be modeled by a $
hi$-ALOHA receiver, we derive outer bounds for the stability region of CPRs, which guarantee that every packet can be successfully received with a probability of 1. Our outer bounds extend those of the spatially-coupled Irregular Repetition Slotted ALOHA (IRSA) protocol and are applicable to channel models with multiple traffic classes. Like convolutional Low-Density Parity-Check (LDPC) codes and the spatially coupled IRSA, we prove that the stability region is not smaller than that of the conventional CPR and it converges as the number of stages of CCPRs goes to infinity. For CCPRs with a single class of users, such a stability region is reduced to an interval and it can be characterized by a percolation threshold. By deriving the potential function of the base CPR used for the construction of a CCPR, we prove that the CCPR is stable if the offered load is below its percolation threshold (under a technical condition for the window size). For the multiclass scenario, we recursively evaluate the density evolution equations to determine the boundaries of the stability region. Numerical results demonstrate that the stability region of CCPRs can be enlarged compared to that of CPRs by leveraging the spatial coupling method.

[1] C.-P. Li, J. Jiang, W. Chen, T. Ji, and J. Smee, “5G ultra-reliable
and low-latency systems design,” in Networks and Communications
(EuCNC), 2017 European Conference on. IEEE, 2017, pp. 1–5.
[2] M. Bennis, M. Debbah, and H. V. Poor, “Ultrareliable and lowlatency
wireless communication: Tail, risk, and scale,” Proceedings
of the IEEE, vol. 106, no. 10, pp. 1834–1853, 2018.
[3] P. Popovski, Cˇ . Stefanovic´, J. J. Nielsen, E. De Carvalho,
M. Angjelichinoski, K. F. Trillingsgaard, and A.-S. Bana, “Wireless
access in ultra-reliable low-latency communication (URLLC),”
IEEE Transactions on Communications, vol. 67, no. 8, pp. 5783–
5801, 2019.
[4] T.-K. Le, U. Salim, and F. Kaltenberger, “An overview of physical
layer design for Ultra-Reliable Low-Latency Communications in
3GPP Releases 15, 16, and 17,” IEEE Access, 2020.
[5] P. Popovski, K. F. Trillingsgaard, O. Simeone, and G. Durisi,
“5G wireless network slicing for eMBB, URLLC, and mMTC: A
communication-theoretic view,” Ieee Access, vol. 6, pp. 55 765–
55 779, 2018.
[6] A. Anand, G. De Veciana, and S. Shakkottai, “Joint scheduling of
URLLC and eMBB traffic in 5G wireless networks,” IEEE/ACM
Transactions on Networking, vol. 28, no. 2, pp. 477–490, 2020.
[7] E. Casini, R. De Gaudenzi, and O. D. R. Herrero, “Contention resolution
diversity slotted ALOHA (CRDSA): An enhanced random
access schemefor satellite access packet networks,” IEEE Transactions
on Wireless Communications, vol. 6, no. 4, 2007.
[8] G. Liva, “Graph-based analysis and optimization of contention resolution
diversity slotted ALOHA,” IEEE Transactions on Communications,
vol. 59, no. 2, pp. 477–487, 2011.
[9] K. R. Narayanan and H. D. Pfister, “Iterative collision resolution for
slotted ALOHA: An optimal uncoordinated transmission policy,” in
Turbo Codes and Iterative Information Processing (ISTC), 2012 7th
International Symposium on. IEEE, 2012, pp. 136–139.
[10] E. Paolini, G. Liva, and M. Chiani, “Random access on graphs:
A survey and new results,” in Signals, Systems and Computers
(ASILOMAR), 2012 Conference Record of the Forty Sixth Asilomar
Conference on. IEEE, 2012, pp. 1743–1747.
[11] E. Paolini, C. Stefanovi´c, G. Liva, and P. Popovski, “Coded random
access: applying codes on graphs to design random access proto-
cols,” IEEE Communications Magazine, vol. 53, no. 6, pp. 144–
150, 2015.
[12] D. Jakoveti´c, D. Bajovi´c, D. Vukobratovi´c, and V. Crnojevi´c, “Cooperative
slotted aloha for multi-base station systems,” IEEE Transactions
on Communications, vol. 63, no. 4, pp. 1443–1456, 2015.
[13] Z. Sun, Y. Xie, J. Yuan, and T. Yang, “Coded slotted ALOHA for
erasure channels: Design and throughput analysis,” IEEE Transactions
on Communications, vol. 65, no. 11, pp. 4817–4830, 2017.
[14] Cˇ . Stefanovic´ and D. Vukobratovic´, “Coded random access,” in Network
Coding and Subspace Designs. Springer, 2018, pp. 339–359.
[15] R. Hoshyar, F. P. Wathan, and R. Tafazolli, “Novel low-density
signature for synchronous CDMA systems over AWGN channel,”
IEEE Transactions on Signal Processing, vol. 56, no. 4, pp. 1616–
1626, 2008.
[16] H. Nikopour and H. Baligh, “Sparse code multiple access,” in Personal
Indoor and Mobile Radio Communications (PIMRC), 2013
IEEE 24th International Symposium on. IEEE, 2013, pp. 332–
336.
[17] Z. Yuan, G. Yu, W. Li, Y. Yuan, X. Wang, and J. Xu, “Multi-user
shared access for Internet of Things,” in Vehicular Technology Conference
(VTC Spring), 2016 IEEE 83rd. IEEE, 2016, pp. 1–5.
[18] S. Chen, B. Ren, Q. Gao, S. Kang, S. Sun, and K. Niu, “Pattern di-
vision multiple access—a novel nonorthogonal multiple access for
fifth-generation radio networks,” IEEE Transactions on Vehicular
Technology, vol. 66, no. 4, pp. 3185–3196, 2017.
[19] O. Ordentlich and Y. Polyanskiy, “Low complexity schemes for the
random access Gaussian channel,” in 2017 IEEE International Symposium
on Information Theory (ISIT). IEEE, 2017, pp. 2528–2532.
[20] A. Vem, K. R. Narayanan, J.-F. Chamberland, and J. Cheng, “A
user-independent successive interference cancellation based coding
scheme for the unsourced random access gaussian channel,” IEEE
Transactions on Communications, vol. 67, no. 12, pp. 8258–8272,
2019.
[21] K. Andreev, E. Marshakov, and A. Frolov, “A polar code based TINSIC
scheme for the unsourced random access in the quasi-static fading
MAC,” in 2020 IEEE International Symposium on Information
Theory (ISIT). IEEE, 2020, pp. 3019–3024.
[22] C.-H. Yu, L. Huang, C.-S. Chang, and D.-S. Lee, “Poisson receivers:
a probabilistic framework for analyzing coded random access,”
IEEE/ACM Transactions on Networking, vol. 29, no. 2, pp.
862–875, 2021.
[23] C.-M. Chang, Y.-J. Lin, C.-S. Chang, and D.-S. Lee, “On the stability
regions of coded poisson receivers with multiple classes of users
and receivers,” IEEE/ACM Transactions on Networking, 2022.
[24] A. Ashikhmin, G. Kramer, and S. ten Brink, “Extrinsic information
transfer functions: model and erasure channel properties,” IEEE
Transactions on Information Theory, vol. 50, no. 11, pp. 2657–
2673, 2004.
[25] Cˇ . Stefanovic´, E. Paolini, and G. Liva, “Asymptotic performance of
coded slotted ALOHA with multipacket reception,” IEEE Communications
Letters, vol. 22, no. 1, pp. 105–108, 2017.
[26] T.-H. Liu, C.-H. Yu, Y.-J. Lin, C.-M. Chang, C.-S. Chang, and D.-S.
Lee, “ALOHA receivers: a network calculus approach for analyzing
coded multiple access with SIC,” IEEE/ACM Transactions on
Networking, vol. 29, no. 2, pp. 862–875, 2021.
[27] S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation
via spatial coupling: Why convolutional LDPC ensembles
perform so well over the BEC,” IEEE Transactions on Information
Theory, vol. 57, no. 2, pp. 803–834, 2011.
[28] A. Yedla, Y.-Y. Jian, P. S. Nguyen, and H. D. Pfister, “A simple
proof of threshold saturation for coupled scalar recursions,” in 2012
7th International Symposium on Turbo Codes and Iterative Information
Processing (ISTC). IEEE, 2012, pp. 51–55.
[29] D. G. Mitchell, M. Lentmaier, and D. J. Costello, “Spatially coupled
LDPC codes constructed from protographs,” IEEE Transactions on
Information Theory, vol. 61, no. 9, pp. 4866–4889, 2015.
[30] G. Liva, E. Paolini, M. Lentmaier, and M. Chiani, “Spatiallycoupled
random access on graphs,” in 2012 IEEE International
Symposium on Information Theory Proceedings. IEEE, 2012, pp.
478–482.
[31] M. Xu, D. Zeng, Z. Sheng, Z. Zhang, and C. Xu, “Some results
on density evolution of nonbinary sc-ldpc ensembles over the
bec,” IEEE International Symposium on Information Theory (ISIT),
vol. 90, pp. 90–95, 2021.
[32] P. S. N. A. Yedla, Y. Y. Jian and H. D. Pfister, “A simple proof
of threshold saturation for coupled vector recursions,” 2012 IEEE
Information Theory Workshop, pp. 25–29, 2012.
[33] C. Schlegel and M. Burnashev, “Thresholds of spatially coupled
systems via lyapunov’s method,” 2013 IEEE Information Theory
Workshop (ITW), pp. 1–5, 2013.
[34] N. Abramson, “THE ALOHA SYSTEM: another alternative for
computer communications,” in Proceedings of the November 17-19,
1970, fall joint computer conference. ACM, 1970, pp. 281–285.
[35] Cˇ . Stefanovic´, M. Momoda, and P. Popovski, “Exploiting capture
effect in frameless ALOHA for massive wireless random access,” in
2014 IEEE Wireless Communications and Networking Conference
(WCNC). IEEE, 2014, pp. 1762–1767.
[36] F. Clazzer, E. Paolini, I. Mambelli, and Cˇ . Stefanovic´, “Irregular
repetition slotted ALOHA over the Rayleigh block fading channel
with capture,” in 2017 IEEE International Conference on Communications
(ICC). IEEE, 2017, pp. 1–6.
[37] M. Ghanbarinejad and C. Schlegel, “Irregular repetition slotted
ALOHA with multiuser detection,” in 2013 10th Annual Conference
on Wireless On-demand Network Systems and Services
(WONS). IEEE, 2013, pp. 201–205.
[38] A. Glebov, N. Matveev, K. Andreev, A. Frolov, and A. Turlikov,
“Achievability bounds for T-fold irregular repetition slotted
ALOHA scheme in the Gaussian MAC,” in 2019 IEEE Wireless
Communications and Networking Conference (WCNC). IEEE,
2019, pp. 1–6.
[39] Z. Chen, Y. Feng, C. Feng, L. Liang, Y. Jia, and T. Q. Quek, “Analytic
distribution design for irregular repetition slotted ALOHA
with multi-packet reception,” IEEE Transactions on Vehicular
Technology, 2022.
[40] M. Luby, M. Mitzenmacher, and M. A. Shokrollahi, “Analysis of
random processes via and-or tree evaluation,” in SODA, vol. 98,
1998, pp. 364–373.
[41] E. Paolini, G. Liva, and M. Chiani, “Graph-based random access for
the collision channel without feedback: Capacity bound,” in 2011
IEEE Global Telecommunications Conference-GLOBECOM 2011.
IEEE, 2011, pp. 1–5.
[42] X. Shao, Z. Sun, M. Yang, S. Gu, and Q. Guo, “NOMA-based irregular
repetition slotted ALOHA for satellite networks,” IEEE Communications
Letters, vol. 23, no. 4, pp. 624–627, 2019.
[43] Y.-C. Huang, S.-L. Shieh, Y.-P. Hsu, and H.-P. Cheng, “Iterative
collision resolution for slotted ALOHA with NOMA for heterogeneous
devices,” IEEE Transactions on Communications, vol. 69,
no. 5, pp. 2948–2961, 2021.
[44] M. Fernández-Veiga, M. Sousa-Vieira, A. Fernández-Vilas, and
R. P. Dáz-Redondo, “Irregular repetition slotted aloha with multiuser
detection: A density evolution analysis,” Computer Networks,
2023.
[45] M. Luby, M. Mitzenmacher, A. Shokrollah, and D. Spielman,
“Analysis of low density codes and improved designs using irregular
graphs,” in Proceedings of the thirtieth annual ACM symposium
on Theory of computing, 1998, pp. 249–258.
[46] T. J. Richardson and R. L. Urbanke, “The capacity of low-density
parity-check codes under message-passing decoding,” IEEE Transactions
on Information Theory, vol. 47, no. 2, pp. 599–618, 2001.
[47] F. P. Kelly, Reversibility and stochastic networks. Cambridge University
Press, 2011.
[48] J. Walrand, “A probabilistic look at networks of quasi-reversible
queues,” IEEE Transactions on Information Theory, no. 6, pp. 825–
831, 1983.
[49] F. P. Kelly, “Loss networks,” The annals of applied probability, pp.
319–378, 1991.