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研究生： 柯凱薰
Ko, Kai-Hsun
論文名稱： 里德所羅門碼與迴旋碼組成之串接碼在URLLC的適用性研究
A Study of Concatenated Reed-Solomon Convolutional Codes for 5G Ultra-Reliable and Low-Latency Communications
指導教授： 呂忠津
Lu, Chung-Chin
口試委員: 蘇育德
Su, Yu T.
蘇賜麟
Su, S.-L.
林茂昭
Lin, Mao-Chao
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 63
中文關鍵詞： 里德所羅門碼 、迴旋碼 、串接碼 、低延遲 、高可靠度
外文關鍵詞： Reed-Solomon, concatenated
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    • 5G又稱為第五代行動網路，為第四代行動網路(4G)的延伸。不同於以往主要
    追求傳輸速度的前幾代，第五代行動網路主要分為三個方向：增強型行動寬
    頻(eMBB)、超可靠低延遲通訊(URLLC)，以及大規模機器型通訊 (mMTC)，以
    提供越來越多樣化的場景使用。其中URLLC對於高可靠度和低延遲的嚴格要
    求是目前一大難題，因為在滿足其中一項要求的同時往往會犧牲了另一個。
    然而，不同於前幾代的行動通訊網路，URLLC對於傳輸速度的要求並不高，
    因此我們想試試看較久沒被拿出來討論的里德所羅門碼(Reed-Solomon code)及
    里德所羅門碼與迴旋碼組成之串接碼(concatenated Reed-Solomon convolutional
    code)在這方面的表現是否良好。本篇論文主要在找出能使里德所羅門碼與迴
    旋碼組成之串接碼的解碼延遲較低的方式，並且比較不同傳輸速度及不同多路
    徑檢測方式下的可靠度。

    This thesis focuses on channel coding particularly for URLLC use case of 5G and evaluating the performance of Reed-Solomon codes and concatenated Reed-Solomon convolutional codes over multipath fading channels. In terms of decoding latency, we find that Reed-Solomon codes perform poorly when the code length is long and the
    code rate is low. Therefore, we bring in concatenated Reed-Solomon convolutional codes to reduce the latency. In terms of reliability, in addition to the concatenated coding scheme, we compare two methods for the detection of signals over multipath fading channels, which are maximum likelihood sequential estimation (MLSE) and orthogonal frequency division multiplexing (OFDM). With the constraint on the detection complexity, we find that MLSE performs better at low to medium data rates, while OFDM performs better at high data rates.

    1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Requirements for 5G-URLLC Scenarios . . . . . . . . . . . . . . . 7 3 Introduction to Concatenated Reed-Solomon Convolutional Codes . . 9 3.1 Introduction to Reed-Solomon Codes . . . . . . . . . . . . . . . 9 3.1.1 Mathematical Properties . . . . . . . . . . . . . . . . . . . 10 3.1.2 Encoding Structure . . . . . . . . . . . . . . . . . . . . . 10 3.1.3 Decoding Structure . . . . . . . . . . . . . . . . . . . . . 11 3.1.4 An Example . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Introduction to Convolutional Codes . . . . . . . . . . . . . . 14 3.2.1 Mathematical Properties . . . . . . . . . . . . . . . . . . . 14 3.2.2 Encoding Structure . . . . . . . . . . . . . . . . . . . . . 15 3.2.3 Decoding Structure . . . . . . . . . . . . . . . . . . . . . 16 4 Multipath Fading Channels . . . . . . . . . . . . . . . . . . . . 20 4.1 Multipath Effect . . . . . . . . . . . . . . . . . . . . . . . 20 4.2 Time-variant Effect . . . . . . . . . . . . . . . . . . . . . . 21 4.3 Generic Mathematical Models . . . . . . . . . . . . . . . . . . 22 4.4 Equivalent Tapped-delay-line Channel Models . . . . . . . . . . 23 4.5 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5 Detection over Multipath Fading Channels . . . . . . . . . . . . 28 5.1 Maximum Likelihood Sequential Estimation . . . . . . . . . . . 28 5.1.1 Received Signal . . . . . . . . . . . . . . . . . . . . . . . 28 5.1.2 Detector with Viterbi Algorithm . . . . . . . . . . . . . . . 29 5.2 Orthogonal Frequency Division Multiplexing (OFDM) . . . . . . . 32 5.2.1 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . 35 6 Decoding Latency of Concatenated Reed-Solomon Convolutional Codes 38 6.1 Decoding Latency of Reed-Solomon Codes . . . . . . . . . . . . 38 6.1.1 A Horner’s Loop . . . . . . . . . . . . . . . . . . . . . . . 39 6.1.2 Early-Stopped Berlekamp–Massey Algorithm . . . . . . . . . . 40 6.1.3 Chien Search . . . . . . . . . . . . . . . . . . . . . . . . 40 6.1.4 Forney’s Algorithm . . . . . . . . . . . . . . . . . . . . . 41 6.1.5 Overall Decoding Latency . . . . . . . . . . . . . . . . . . 41 6.2 Decoding Latency of Convolutional Codes . . . . . . . . . . . . 43 6.3 Decoding Latency of Concatenated Reed-Solomon Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 7 Performance Evaluation for URLLC . . . . . . . . . . . . . . . . 45 7.1 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . 45 7.2 Latency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

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