脈衝超寬頻(IR-UWB)是近年來越來越受到矚目與重視的先進通訊技術。該技術最特別之處在於透過發送奈秒級的脈衝訊號進行通訊，因此，非常適合應用於需要公分級精準度的測距等相關應用。脈衝超寬頻具體應用包括室內定位、免持鑰匙、物品搜尋等。目前已經商用化的產品例如Apple的Air Tag內的U1晶片等也是基於脈衝超寬頻技術。脈衝超寬頻應用的共通之處即為需要對當下環境的情況進行即時反應，否則這些應用將無法發揮效果，因在設計脈衝超寬頻系統時，如何達到低處理延遲是最重要的設計考量，以達到應用系統的即時反應的需求。里德-所羅門碼是超寬頻系統中經常使用的錯誤更正碼，其主要功能為增加冗餘位元讓封包具可修復性，以有效降低封包在傳輸過中因受到干擾而無法正確接收的情況。里德-所羅門碼的元件對於脈衝超寬頻系統整體運算效能有重大影響，因此值得研究探討。本論文基於IEEE 802.15.4a/z規格的脈衝超寬頻系統接收器，設計低延遲與低複雜度的的里德-所羅門碼電路架構。我們提出的架構首先基於平行處理以達到低延遲的運算。此外，由於平行化架構使得電路面積上升，我們進一步也提出了降低面積負責度的電路設計。我們設計的里德-所羅門碼電路架構可以使延遲降低85.7%，而所花費的面積可以降低30%。

Impulse Radio Ultra-Wideband (IR-UWB) communication technology has gained increasing attention recently. Its distinct feature is that it utilizes nanosecond-level pulses for communication. Therefore, UWB is particularly well-suited for developing applications related to distance measurement, with precision that can even reach centimeter-level accuracy. Relevant applications include indoor positioning, keyless entry, and item tracking. Commercial products incorporating UWB technology, such as Apple's AirTag with the U1 Chip, are already available. The common requirement among these applications is real-time responsiveness to the current environmental conditions. Without low-latency design, these applications would not be able to function effectively. Therefore, low latency is crucial for UWB systems. RS codes in UWB systems are responsible for adding redundant bits to make packets error-correctable, effectively reducing the likelihood of packets being incorrectly received due to interference during transmission. Hence, this paper addresses the RS decoder of the IEEE 802.15.4a/z HRP UWB PHY receiver and presents a low-latency architecture through parallelization. In addition, as parallelization increases circuit area, optimized area-efficient circuit designs are proposed. With the implementation of 16-stage parallelization, it reduces latency by 85.7% and achieves a 30% reduction in the required area.

[1] “IEEE Standard for Low-Rate Wireless Networks,” IEEE Std 802.15.4-2020 (Revision of IEEE Std 802.15.4-2015), pp. 1–800, 2020.

[2] A. El Gueraa, A. Darif, R. Saadane, and D. Aboutajdine, “An efficient transceiver for vehicular ad hoc network based on ir-uwb,” in 2014 Second World Conference on Complex Systems (WCCS), 2014, pp. 220–224.

[3] H.-B. Li, R. Miura, T. Kagawa, F. Kojima, and H. Nishikawa, “Improvement of receiver sensitivity for enhancing ir-uwb performance for indoor positioning,” in 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), 2017, pp. 1–5.

[4] J.-E. Kim, J.-H. Choi, and K.-T. Kim, “Robust detection of presence of individuals in an indoor environment using ir-uwb radar,” IEEE Access, vol. 8, pp. 108 133–108 147, 2020.

[5] “IEEE Standard for Low-Rate Wireless Networks–Amendment 1: Enhanced Ultra Wideband (UWB) Physical Layers (PHYs) and Associated Ranging Techniques,” IEEE Std 802.15.4z-2020 (Amendment to IEEE Std 802.15.4-2020), pp. 1–174, 2020.

[6] D. Coppens, A. Shahid, S. Lemey, B. Van Herbruggen, C. Marshall, and E. De Poorter, “An Overview of UWB Standards and Organizations (IEEE 802.15.4, FiRa, Apple): Interoperability Aspects and Future Research Directions,” IEEE Access, vol. 10, pp. 70 219–70 241, 2022.

[7] “Nearby Interaction with UWB,” accessed: May 2023. [Online]. Available: https://developer.apple.com/nearby-interaction/

[8] “Qorvo. DW1000,” accessed: May 2023. [Online]. Available: https://www.qorvo.com/products/p/DW1000

[9] “Qorvo. DW3110,” accessed: May 2023. [Online]. Available: https://www.qorvo.com/products/p/DW3110

[10]P. Mayer, M. Magno, C. Schnetzler, and L. Benini, “Embeduwb: Low power embedded high-precision and low latency uwb localization,” in 2019 IEEE 5th World Forum on Internet of Things (WF-IoT), 2019, pp. 519–523.

[11] I. S. Reed and G. Solomon, “Polynomial codes over certain finite fields," Journal of the society for industrial and applied mathematics, vol. 8, no. 2, pp. 300–304, 1960.

[12] R. C. Bose and D. K. Ray-Chaudhuri, “On a class of error correcting binary group codes,” Information and control, vol. 3, no. 1, pp. 68–79, 1960

[13] S.-W. Choi, S.-S. Choi, and H. ho Lee, “Rs decoder architecture for uwb,” in 2006 8th International Conference Advanced Communication Technology, vol. 1, 2006, pp. 4 pp.–808.

[14] B. Chen, X. Zhang, and Z. Wang, “Error correction for multi-level nand flash memory using reed solomon codes,” in 2008 IEEE Workshop on Signal Processing Systems, 2008, pp. 94–99.

[15] C. Kim, S. Rhee, J. Kim, and Y. Jee, “Product reed-solomon codes for implementing nand flash controller on fpga chip,” in 2010 Second International Conference on Computer Engineering and Applications, vol. 1, 2010, pp. 281–285.

[16] B. Zheng, C. Condo, W. J. Gross, and O. Liboiron-Ladouceur, “High -throughput low-latency encoder and decoder for a class of generalized reed -solomon codes for short-reach optical communications,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 4, pp. 670–674, 2020.

[17] B. Yuan, Z. Wang, L. Li, M. Gao, J. Sha, and C. Zhang, “Area-efficient reed-solomon decoder design for optical communications,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 56, no. 6, pp. 469–473, 2009.

[18] R. E. Blahut, “Theory and practice of error control codes,” (No Title), 1983.

[19] H. A. E. A. Elsaid, “Design and implementation of reed-solomon decoder using decomposed inversion less berlekamp-massey algorithm,” Faculty of Engineering, Cairo University, Giza, Egypt, 2010.

[20] E. R. Berlekamp, Algebraic coding theory (revised edition). World Scientific, 2015.

[21] Y. Sugiyama, M. Kasahara, S. Hirasawa, and T. Namekawa, “A method for solving key equation for decoding goppa codes,” Information and Control, vol. 27, no. 1, pp. 87–99, 1975.

[22] S. Gao, “A new algorithm for decoding reed-solomon codes,” in Communications, information and network security. Springer, 2003, pp. 55–68.

[23] D. Sarwate and N. Shanbhag, “High-speed architectures for reed -solomon decoders,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 9, no. 5, pp. 641–655, 2001.

[24] R. Chien, “Cyclic decoding procedures for bose-chaudhuri-hocquenghem codes,” IEEE Transactions on information theory, vol. 10, no. 4, pp. 357–363, 1964.

[25] G. Forney, “On decoding bch codes,” IEEE Transactions on Information Theory, vol. 11, no. 4, pp. 549–557, 1965.

[26] J. Massey, “Step-by-step decoding of the bose-chaudhuri-hocquenghem codes,” IEEE Transactions on Information Theory, vol. 11, no. 4, pp. 580–585, 1965.

[27] H. Burton, “Inversionless decoding of binary bch codes,” IEEE Transactions on Information Theory, vol. 17, no. 4, pp. 464–466, 1971.

[28] J. Samanta, J. Bhaumik, and S. Barman, “Compact rs(32, 28) encoder,” in Intelligent Computing and Applications, D. Mandal, R. Kar, S. Das, and B. K. Panigrahi, Eds. New Delhi: Springer India, 2015, pp. 89–95.

[29] J. Samanta and J. Bhaumik, “Fpga based area efficient rs(23, 17) codec,” Microsystem Technologies, vol. 23, pp. 639–650,2017.