CMC

Color Multiset Coding (CMC)

Introduction

Color multiset coding (a.k.a. Grid color coding) is defined over a source symbol set arranged in an n-dimensional cyclic or flat integer lattice, exploiting the grid topology for coding and decoding. It maps source symbols into multisets of an alphabet instead of ordered sequences. We refer to the mapping as a color mapping and the code as a color multiset code (CMC).

Application and Use Case

Such a formulation of source coding is an alternative approach to the traditional framework and was inspired by object tracking problem over wireless IoT network [R6: App. 18/764,911] and light based positioning system [R7: hal-05367398].

Example 1: Proximity Sensor Network & Smart Infrastructure [App. 18/764,911] 

Example 2: Light Based Positioning System [hal-05367398]

Talks

  1. Y.-H. Lo, “Multiset Combinatorial Gray Codes and Universal Cycles,” presented at Annual Meeting of Taiwanese Mathematical Society (TMS), 2025. [Slide]
  2. Y.-H. Lo, “Object Tracking Using Multiset Color Coding,” presented at ISITA Conference, 2024. [Slide]
  3. C. S. Chen, “Object Tracking Using Multiset Combinatorial Gray Code,” presented at HKMU CRANT Talk Series, 2024.
  4. E. de Panafieu, “Robot Positioning Using Torus Packing for Multisets,” presented at ICALP Conference, 2024. [Slide]

Software

  1. A. Pang, “C2-SeqRL: Reinforcement learning for conflict-constrained sequence construction,” 2025. [Code]
  2. Y.-H. Lo, “Color multiset codes based on sunmao construction,” 2025. [Code]
  3. E. de Panafieu, “Robot positioning using torus packing for multisets,” 2024. [Code]

Publications and Related 

  1. W. S. Wong, C. S. Chen, and Y.-H. Lo, “Color multiset codes based on sunmao construction,” Preprint, 2025. [arXiv:2511.09070v1]
  2. C. S. Chen, W. S. Wong, Y.-H. Lo, and T.-L. Wong, “Multiset combinatorial Gray codes with application to proximity sensor networks,” Preprint, 2025. [arXiv:2410.15428v2]
  3. A. Pang, C. S. Chen, M. Wang, M.-O. Pun, Y.-H. Lo, and W. S. Wong, “C2-SeqRL: Reinforcement learning for conflict-constrained sequence construction,” IEEE 25th International Conference on Electronics, Information, and Communication, 2026. [hal-05366346] [Code]
  4. C. S. Chen, Y.-H. Lo, W. S. Wong, and Y. Zhang, “Object tracking using multiset color coding,” Intl. Symp. on Information Theory and Its Applications (ISITA), 2024. [hal-05367395]
  5. C. S. Chen, P. Keevash, W. S. Kennedy, E. de Panafieu, and A. Vetta, “Robot positioning using torus packing for multisets,” 51st EATCS Intl. Colloquium on Automata, Languages and Programming (ICALP), 2024. [arXiv:2404.09981v1]
  6. C. S. Chen, P. Baracca, E. De Panafieu, and D. Michalopoulos, “Positioning approach,” Patent, 2024. [App. 18/764,911]
  7. S.-W. Ho and C. S. Chen, “Visible light communication based positioning using color sensor,” IEEE Optoelectronics Global Conference (OGC), Best Paper Award & Optoelectronic Technology Innovation Award, 2023. [hal-05367398]

Literature & Prior Art (Part) 

  1. N. G. De Bruijn, “A combinatorial problem,” Proceedings of the Section of Sciences of the Koninklijke Nederlandse Akademie van Wetenschappen te Amsterdam, vol. 49, no. 7, pp. 758–764, 1946.
  2. F. W. Sinden, “Sliding window codes,” AT&T Bell Laboratories Technical Memorandum, pp. 1–19, 1985.
  3. W. D. Blizard, “Multiset theory,” Notre Dame Journal of Formal Logic, vol. 30, no. 1, pp. 36–66, 1989.
  4. F. Chung, P. Diaconis, and R. Graham, “Universal cycles for combinatorial structures,” Discrete Math., vol. 110, pp. 43–59, 1992.
  5. P. Kumar and V. Wei, “Minimum distance of logarithmic and fractional partial m-sequences,” IEEE Transactions on Information Theory, vol. 38, no. 5, pp. 1474–1482, 1992.
  6. C. Savage, “A survey of combinatorial Gray codes,” SIAM Review, vol. 39, no. 4, pp. 605–629, 1997.
  7. C. J. Mitchell and P. R. Wild, “Constructing orientable sequences,” IEEE Transactions on Information Theory, vol. 68, no. 7, pp. 4782–4789, 2022.
  8. T. Etzion, Sequences and the de Bruijn Graph: Properties, Constructions, and Applications, Academic Press, 2024.

Acknowledgement

Cédric Adjih, INRIA
Paolo Baracca, Nokia
Marc-Olivier Buob, Nokia Bell Labs
Elie De Panafieu, Nokia Bell Labs
Siu-Wai Ho, University of Adelaide
Peter Keevash, University of Oxford
Sean Kennedy, Nokia Bell Labs
Fang Liu, Shenzhen University
Simon Pun, The Chinese University of Hong Kong, Shenzhen
Kenneth Shum, The Chinese University of Hong Kong, Shenzhen
Adrian Vetta, McGill University
Yijin Zhang, Nanjing University of Science and Technology
The National Science and Technology Council of Taiwan (Grants NSTC 114-2628-M-153-001-MY3, Principal Investigator: Yuan-Hsun Lo, National Pingtung University)

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