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研究生： 劉泰泉
BENJAMIN LIU
論文名稱： 優化在干擾通道並使用有限長度之球型碼的情況下雙用戶的速率和
Sum Rate Optimization in 2-user Interference Channel Using Spherical Codebook in Finite block-length Regime
指導教授： 林益如
Yi-Ru Lin
口試委員: 林士駿
Shih-Chun Lin
謝松年
Sung-Nien Hsieh
學位類別： 碩士
Master
系所名稱： 電資學院 - 電子工程系
Department of Electronic and Computer Engineering
論文出版年： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 88
中文關鍵詞： 有限長度碼 、球型碼 、混和式單調規劃 、優化 、高可靠度和低時延通訊 、干擾通道 、速率和
外文關鍵詞： FBC, Spherical Codebook, MMP, Optimization, URLLC, Interference Channel, Sum Rate
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    • 在本篇論文中，我們會討論在有限長度碼長及使用球型碼的傳輸速率。並且我們還找了這個速率之下界的簡單形式。我們主要的貢獻是證明這兩個速率均為混和式單調規劃。在這篇的這個數學式子因為碼常有限長的關係多出了發散項，因此在證明有混和式單調規劃之特性事上，相較於傳統夏農通道容量，會複雜許多。

    In this paper, we will discuss the rate in finite block-length regime using spherical codebook. Also we found a lower bound of the rate for a simpler form. Based on two rates above, our main work is proving that both rates are mixed monotonic (MM) function. The form of the rate we used in this paper is more complicated to prove its M property than traditional Shannon capacity due to the additional dispersion term is added cause by the finiteness of block-length.

    Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . iii Contents . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Figures . . . . . . . . . . . . . . . . . . . . . . vi List of Algorithms . . . . . . . . . . . . . . . . . . . . vii Notation . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 Introduction . . . . . . . . . . . . . . . . . . . . . 1 2 2-user interference channel . . . . . . . . . . . . . 3 3 Concept of codebook . . . . . . . . . . . . . . . . 4 3.1 i.i.d. Gaussian codebook . . . . . . . . . . . 5 3.2 Spherical Gaussian codebook . . . . . . . . . 6 4 Channel coding rate in finite blocklength regime . . 7 4.1 Rate for both users use i.i.d. Gaussian codebook 8 4.2 Rate for both users use spherical Gaussian codebook . . . . . . . . . . . . . . . . . . . . . . 9 4.2.1 Lower rate of shell rate . . . . . . . . 9 5 Sum Rate Optimization Problem . . . . . . . . . . 11 5.1 Mixed Motonic Programming . . . . . . . . 12 iv 5.2 Sum Rate Optimization Problem of MMP form 17 6 Simulation Results . . . . . . . . . . . . . . . . . . 20 7 Conclusions . . . . . . . . . . . . . . . . . . . . . 24 7.1 Future Work . . . . . . . . . . . . . . . . . . 24 Appendix A: Rate comparison . . . . . . . . . . . . . 25 Appendix B: PROOF OF MONOTONICITY OF FBC RATE AS USERS BOTH USE SPHERICAL CODBOOK . . . . . . . . . . . . . . . . . . . . . . . . 27 Appendix C: PROOF OF MONOTONICITY OF FBC RATE AS USERS BOTH USE SPHERICAL CODEBOOK . . . . . . . . . . . . . . . . . . . . . . . . 30 Appendix D: PROOF OF MONOTONICITY OF THEOREM 5.1.4 . . . . . . . . . . . . . . . . . . . . . 61 Appendix E: PROOF OF MONOTONICITY OF FBC RATE AS USERS BOTH USE SPHERICAL CODEBOOK BUT WITH LOWER RATE . . . . . . . . 65 Appendix F: PROOF OF MONOTONICITY OF THEOREM 5.1.6 . . . . . . . . . . . . . . . . . . . . . 76 References . . . . . . . . . . . . . . . . . . . . . . . . 78

    [1] V. S. Annapureddy and V. V. Veeravalli, “Gaussian interference networks: Sum capacity in the lowinterference regime and new outer bounds on the capacity region,” IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3032–3050, 2009.
    [2] G. Durisi, T. Koch, and P. Popovski, “Toward massive, ultrareliable, and low-latency wireless communication with short packets,” Proceedings of the IEEE, vol. 104, no. 9, pp. 1711–1726, 2016.
    [3] B. Matthiesen, C. Hellings, E. A. Jorswieck, and W. Utschick, “Mixed monotonic programming for fast global optimization,” IEEE Transactions on Signal Processing, vol. 68, pp. 2529–2544, 2020.
    [4] Y. Polyanskiy, H. V. Poor, and S. Verdú, “Channel coding rate in the finite blocklength regime,” IEEE Transactions on Information Theory, vol. 56, no. 5, pp. 2307–2359, 2010.
    [5] J. Scarlett, V. Y. Tan, and G. Durisi, “The dispersion of nearest-neighbor decoding for additive nongaussian channels,” IEEE Transactions on Information Theory, vol. 63, no. 1, pp. 81–92, 2016.

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