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Information Mathematics (Hagiwara) Lab
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Using the power of mathematics to build systems that find and correct errors.
AboutAbout the lab
Mathematics that can recover from errors.
The Hagiwara Lab studies coding theory, which treats error correction as a branch of mathematics.
Coding theory is used in devices and technologies such as smartphones, QR codes, DVDs, and wireless LANs.
The lab also works on discrete mathematics, which examines combinatorial structures and enumeration.
While keeping industrial applications in mind, the lab values the joy of pure theory.
Key terms
- coding theory
- A field that uses mathematics to study mechanisms for detecting and correcting errors that occur during communication or recording
- discrete mathematics
- Mathematics that deals with discrete values and combinations. It studies enumeration and combinatorial structures
- deletion error
- A type of error in which a symbol drops out partway through the data, shifting the sequence that follows
ResearchResearch themes
Centered on coding theory, the lab aims to develop mathematics with industrial applications in mind. Its research rests on two pillars: the theory of error correction, and discrete mathematics dealing with combinatorial structures and enumeration.
*Illustrative imageDiscrete Mathematics and Enumeration
The lab is interested in combinatorial structures and enumeration. As in the problem of counting combinations of variables that each take the value 0 or 1, the questions are simple but the answers are complex, and a variety of mathematics is used along the way to derive them.
*Illustrative imageCoding Theory and Error Correction
Coding theory treats errors such as mishearing or miswriting as an object of mathematics. It is used in smartphones, QR codes, DVDs, and wireless LANs, and the more the theory advances, the more new applications emerge.
*Illustrative imageCodes for Correcting Quantum Insertions and Deletions
The lab was the first in the world to discover both codes that can correct quantum deletion errors and codes that can correct quantum insertion errors. Both papers have received awards.
MembersFaculty
- ProfessorManabu Hagiwara
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “DataMatrix 144x144 Lorem” Blockpolymer / CC BY-SA 4.0 (cropped)
- Discrete Mathematics and Enumeration: “EN- Reverse sort 1” PChlosta / CC BY-SA 4.0 (cropped)
- Coding Theory and Error Correction: “DVD+R with Data” Zi7ar21 / CC0 (cropped)
- Codes for Correcting Quantum Insertions and Deletions: “Measuring a qubit leaves no room for error” FMNLab / CC BY 4.0 (cropped)
- Related lab (Mathematical Informatics (Mitsuru Tada) Lab): “Operable Enigma Available to Make Encrypted Messages” crudmucosaz / CC BY 2.0 (cropped)
- Related lab (Algebra (Matsuda) Lab): “Abox - Sphere 4D 8K HQ OpenCL 20200323 klein” PantheraLeo1359531 / CC BY 4.0 (cropped)
- Related lab (Mathematical Informatics Lab): “Atari 800 XL home computer with TV monitor and tape program recorder XC12 (cropped)” winkelnkemper / CC BY-SA 2.0 (cropped)
- Related lab (Information Mathematics (Nakamura) Lab): “Signal flow graph for a digital IIR Biquad” Constant314 / CC0 (cropped)
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