9 Search Results for "Lin, Ting-Chun"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.101
Two Bases Suffice for QMA ₁-Completeness

Authors: Henry Ma and Anand Natarajan

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We introduce a basis-restricted variant of the Quantum-k-Sat problem, in which each term in the input Hamiltonian is required to be diagonal in either the standard or Hadamard basis. Our main result is that the Quantum-6-Sat problem with this basis restriction is already QMA₁-complete, defined with respect to a natural gateset. Our construction is based on the Feynman-Kitaev circuit-to-Hamiltonian construction, with a modified clock encoding that interleaves two clocks in the standard and Hadamard bases. In light of the central role played by CSS codes and the uncertainty principle in the proof of the NLTS theorem of Anshu, Breuckmann, and Nirkhe (STOC '23), we hope that the CSS-like structure of our Hamiltonians will make them useful for progress towards a quantum PCP theorem.
Cite as

Henry Ma and Anand Natarajan. Two Bases Suffice for QMA ₁-Completeness. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 101:1-101:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ma_et_al:LIPIcs.ITCS.2026.101,
  author =	{Ma, Henry and Natarajan, Anand},
  title =	{{Two Bases Suffice for QMA ₁-Completeness}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{101:1--101:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.101},
  URN =		{urn:nbn:de:0030-drops-253880},
  doi =		{10.4230/LIPIcs.ITCS.2026.101},
  annote =	{Keywords: quantum complexity theory, Hamiltonian complexity, Quantum Merlin Arthur (QMA), QMA₁, quantum satisfiability problem}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.60
Total Search Problems in ZPP

Authors: Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We initiate a systematic study of TFZPP, the class of total NP search problems solvable by polynomial time randomized algorithms. TFZPP contains a variety of important search problems such as Bertrand-Chebyshev (finding a prime between N and 2N), refuter problems for many circuit lower bounds, and Lossy-Code. The Lossy-Code problem has found prominence due to its fundamental connections to derandomization, catalytic computing, and the metamathematics of complexity theory, among other areas. While TFZPP collapses to FP under standard derandomization assumptions in the white-box setting, we are able to separate TFZPP from the major TFNP subclasses in the black-box setting. In fact, we are able to separate it from every uniform TFNP class assuming that NP is not in quasi-polynomial time. To do so, we extend the connection between proof complexity and black-box TFNP to randomized proof systems and randomized reductions. Next, we turn to developing a taxonomy of TFZPP problems. We highlight a problem called Nephew, originating from an infinity axiom in set theory. We show that Nephew is in PWPP∩ TFZPP and conjecture that it is not reducible to Lossy-Code. Intriguingly, except for some artificial examples, most other black-box TFZPP problems that we are aware of reduce to Lossy-Code: - We define a problem called Empty-Child capturing finding a leaf in a rooted (binary) tree, and show that this problem is equivalent to Lossy-Code. We also show that a variant of Empty-Child with "heights" is complete for the intersection of SOPL and Lossy-Code. - We strengthen Lossy-Code with several combinatorial inequalities such as the AM-GM inequality. Somewhat surprisingly, we show the resulting new problems are still reducible to Lossy-Code. A technical highlight of this result is that they are proved by formalizations in bounded arithmetic, specifically in Jeřábek’s theory APC₁ (JSL 2007). - Finally, we show that the Dense-Linear-Ordering problem reduces to Lossy-Code.
Cite as

Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan. Total Search Problems in ZPP. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 60:1-60:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{fleming_et_al:LIPIcs.ITCS.2026.60,
  author =	{Fleming, Noah and Grosser, Stefan and Jain, Siddhartha and Li, Jiawei and Ren, Hanlin and Shirley, Morgan and Yuan, Weiqiang},
  title =	{{Total Search Problems in ZPP}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{60:1--60:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.60},
  URN =		{urn:nbn:de:0030-drops-253473},
  doi =		{10.4230/LIPIcs.ITCS.2026.60},
  annote =	{Keywords: TFNP, lossy code, randomized proof systems, query complexity}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.9
Algebra Is Half the Battle: Verifying Presentations of Graded Unipotent Chevalley Groups

Authors: Eric Wang, Arohee Bhoja, Cayden Codel, and Noah G. Singer

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Graded unipotent Chevalley groups are an important family of groups on matrices with polynomial entries over a finite field. Using the Lean theorem prover, we verify that three such groups, namely, the A₃- and the two B₃-type groups, satisfy a useful group-theoretic condition. Specifically, these groups are defined by a set of equations called Steinberg relations, and we prove that a certain canonical "smaller" set of Steinberg relations suffices to derive the rest. Our work is motivated by an application for building topologically-interesting objects called higher-dimensional expanders (HDXs). In the past decade, HDXs have formed the basis for many new results in theoretical computer science, such as in quantum error correction and in property testing. Yet despite the increasing prevalence of HDXs, only two methods of constructing them are known. One such method builds an HDX from groups that satisfy the aforementioned property, and the Chevalley groups we use are (essentially) the only ones currently known to satisfy it.
Cite as

Eric Wang, Arohee Bhoja, Cayden Codel, and Noah G. Singer. Algebra Is Half the Battle: Verifying Presentations of Graded Unipotent Chevalley Groups. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{wang_et_al:LIPIcs.ITP.2025.9,
  author =	{Wang, Eric and Bhoja, Arohee and Codel, Cayden and Singer, Noah G.},
  title =	{{Algebra Is Half the Battle: Verifying Presentations of Graded Unipotent Chevalley Groups}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.9},
  URN =		{urn:nbn:de:0030-drops-246071},
  doi =		{10.4230/LIPIcs.ITP.2025.9},
  annote =	{Keywords: Group presentations, term rewriting, metaprogramming, proof automation, the Lean theorem prover}
}
Document
DOI: 10.4230/OASIcs.SpaceCHI.2025.6
Toward an Earth-Independent System for EVA Mission Planning: Integrating Physical Models, Domain Knowledge, and Agentic RAG to Provide Explainable LLM-Based Decision Support

Authors: Kaisheng Li and Richard S. Whittle

Published in: OASIcs, Volume 130, Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)

Abstract
We propose a unified framework for an Earth‑independent AI system that provides explainable, context‑aware decision support for EVA mission planning by integrating six core components: a fine‑tuned EVA domain LLM, a retrieval‑augmented knowledge base, a short-term memory store, physical simulation models, an agentic orchestration layer, and a multimodal user interface. To ground our design, we analyze the current roles and substitution potential of the Mission Control Center - identifying which procedural and analytical functions can be automated onboard while preserving human oversight for experiential and strategic tasks. Building on this framework, we introduce RASAGE (Retrieval & Simulation Augmented Guidance Agent for Exploration), a proof‑of‑concept toolset that combines Microsoft Phi‑4‑mini‑instruct with a FAISS (Facebook AI Similarity Search)‑powered EVA knowledge base and custom A* path planning and hypogravity metabolic models to generate grounded, traceable EVA plans. We outline a staged validation strategy to evaluate improvements in route efficiency, metabolic prediction accuracy, anomaly response effectiveness, and crew trust under realistic communication delays. Our findings demonstrate the feasibility of replicating key Mission Control functions onboard, enhancing crew autonomy, reducing cognitive load, and improving safety for deep‑space exploration missions.
Cite as

Kaisheng Li and Richard S. Whittle. Toward an Earth-Independent System for EVA Mission Planning: Integrating Physical Models, Domain Knowledge, and Agentic RAG to Provide Explainable LLM-Based Decision Support. In Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025). Open Access Series in Informatics (OASIcs), Volume 130, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{li_et_al:OASIcs.SpaceCHI.2025.6,
  author =	{Li, Kaisheng and Whittle, Richard S.},
  title =	{{Toward an Earth-Independent System for EVA Mission Planning: Integrating Physical Models, Domain Knowledge, and Agentic RAG to Provide Explainable LLM-Based Decision Support}},
  booktitle =	{Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)},
  pages =	{6:1--6:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-384-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{130},
  editor =	{Bensch, Leonie and Nilsson, Tommy and Nisser, Martin and Pataranutaporn, Pat and Schmidt, Albrecht and Sumini, Valentina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SpaceCHI.2025.6},
  URN =		{urn:nbn:de:0030-drops-239967},
  doi =		{10.4230/OASIcs.SpaceCHI.2025.6},
  annote =	{Keywords: Human-AI Interaction for Space Exploration, Extravehicular Activities, Cognitive load and Human Performance Issues, Human Systems Exploration, Lunar Exploration, LLM}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.59
Testing Tensor Products of Algebraic Codes

Authors: Sumegha Garg, Madhu Sudan, and Gabriel Wu

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
Motivated by recent advances in locally testable codes and quantum LDPCs based on robust testability of tensor product codes, we explore the local testability of tensor products of (an abstraction of) algebraic geometry codes. Such codes are parameterized by, in addition to standard parameters such as block length n and dimension k, their genus g. We show that the tensor product of two algebraic geometry codes is robustly locally testable provided n = Ω((k+g)²). Apart from Reed-Solomon codes, this seems to be the first explicit family of two-wise tensor codes of high dual distance that is robustly locally testable by the natural test that measures the expected distance of a random row/column from the underlying code.
Cite as

Sumegha Garg, Madhu Sudan, and Gabriel Wu. Testing Tensor Products of Algebraic Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{garg_et_al:LIPIcs.APPROX/RANDOM.2025.59,
  author =	{Garg, Sumegha and Sudan, Madhu and Wu, Gabriel},
  title =	{{Testing Tensor Products of Algebraic Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{59:1--59:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.59},
  URN =		{urn:nbn:de:0030-drops-244254},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.59},
  annote =	{Keywords: Algebraic geometry codes, Robust testability, Tensor products of codes}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.4
Optimal Locality and Parameter Tradeoffs for Subsystem Codes

Authors: Samuel Dai, Ray Li, and Eugene Tang

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
We study the tradeoffs between the locality and parameters of subsystem codes. We prove lower bounds on both the number and lengths of interactions in any D-dimensional embedding of a subsystem code. Specifically, we show that any embedding of a subsystem code with parameters [[n,k,d]] into R^D must have at least M^* interactions of length at least 𝓁^*, where M^* = Ω(max(k,d)), and 𝓁^* = Ω(max(d/(n^((D-1)/D)), ((kd^(1/(D-1))/n))^((D-1)/D))). We also give tradeoffs between the locality and parameters of commuting projector codes in D-dimensions, generalizing a result of Dai and Li [Dai and Li, 2025]. We provide explicit constructions of embedded codes that show our bounds are optimal in both the interaction count and interaction length.
Cite as

Samuel Dai, Ray Li, and Eugene Tang. Optimal Locality and Parameter Tradeoffs for Subsystem Codes. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dai_et_al:LIPIcs.TQC.2025.4,
  author =	{Dai, Samuel and Li, Ray and Tang, Eugene},
  title =	{{Optimal Locality and Parameter Tradeoffs for Subsystem Codes}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.4},
  URN =		{urn:nbn:de:0030-drops-240539},
  doi =		{10.4230/LIPIcs.TQC.2025.4},
  annote =	{Keywords: Quantum Error Correcting Code, Locality, Subsystem Code, Commuting Projector Code}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.25
Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products

Authors: Louis Golowich and Venkatesan Guruswami

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
The first linear-distance quantum LDPC codes were recently constructed by a line of breakthrough works (culminating in the result of Panteleev & Kalachev, 2021). All such constructions, even when allowing for almost-linear distance, are based on an operation called a balanced (or lifted) product, which is used in a one-shot manner to combine a pair of large classical codes possessing a group symmetry. We present a new construction of almost-linear distance quantum LDPC codes that is iterative in nature. Our construction is based on a more basic and widely used product, namely the homological product (i.e. the tensor product of chain complexes). Specifically, for every ε > 0, we obtain a family of [[N,N^{1-ε},N^{1-ε}]] (subsystem) quantum LDPC codes via repeated homological products of a constant-sized quantum locally testable code. Our key idea is to remove certain low-weight codewords using subsystem codes (while still maintaining constant stabilizer weight), in order to circumvent a particular obstruction that limited the distance of many prior homological product code constructions to at most Õ(√N).
Cite as

Louis Golowich and Venkatesan Guruswami. Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 25:1-25:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{golowich_et_al:LIPIcs.CCC.2025.25,
  author =	{Golowich, Louis and Guruswami, Venkatesan},
  title =	{{Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{25:1--25:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.25},
  URN =		{urn:nbn:de:0030-drops-237196},
  doi =		{10.4230/LIPIcs.CCC.2025.25},
  annote =	{Keywords: Quantum Error Correction, Quantum LDPC Code, Homological Product, Iterative Construction}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.7
Sparser Abelian High Dimensional Expanders

Authors: Yotam Dikstein, Siqi Liu, and Avi Wigderson

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
The focus of this paper is the development of new elementary techniques for the construction and analysis of high dimensional expanders. Specifically, we present two new explicit constructions of Cayley high dimensional expanders (HDXs) over the abelian group 𝔽₂ⁿ. Our expansion proofs use only linear algebra and combinatorial arguments. The first construction gives local spectral HDXs of any constant dimension and subpolynomial degree exp(n^ε) for every ε > 0, improving on a construction by Golowich [Golowich, 2023] which achieves ε = 1/2. [Golowich, 2023] derives these HDXs by sparsifying the complete Grassmann poset of subspaces. The novelty in our construction is the ability to sparsify any expanding Grassmann posets, leading to iterated sparsification and much smaller degrees. The sparse Grassmannian (which is of independent interest in the theory of HDXs) serves as the generating set of the Cayley graph. Our second construction gives a 2-dimensional HDX of any polynomial degree exp(ε n) for any constant ε > 0, which is simultaneously a spectral expander and a coboundary expander. To the best of our knowledge, this is the first such non-trivial construction. We name it the Johnson complex, as it is derived from the classical Johnson scheme, whose vertices serve as the generating set of this Cayley graph. This construction may be viewed as a derandomization of the recent random geometric complexes of [Liu et al., 2023]. Establishing coboundary expansion through Gromov’s "cone method" and the associated isoperimetric inequalities is the most intricate aspect of this construction. While these two constructions are quite different, we show that they both share a common structure, resembling the intersection patterns of vectors in the Hadamard code. We propose a general framework of such "Hadamard-like" constructions in the hope that it will yield new HDXs.
Cite as

Yotam Dikstein, Siqi Liu, and Avi Wigderson. Sparser Abelian High Dimensional Expanders. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 7:1-7:98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dikstein_et_al:LIPIcs.CCC.2025.7,
  author =	{Dikstein, Yotam and Liu, Siqi and Wigderson, Avi},
  title =	{{Sparser Abelian High Dimensional Expanders}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{7:1--7:98},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.7},
  URN =		{urn:nbn:de:0030-drops-237013},
  doi =		{10.4230/LIPIcs.CCC.2025.7},
  annote =	{Keywords: Local spectral expander, coboundary expander, Grassmannian expander}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.17
Accelerating Polarization via Alphabet Extension

Authors: Iwan Duursma, Ryan Gabrys, Venkatesan Guruswami, Ting-Chun Lin, and Hsin-Po Wang

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
Polarization is an unprecedented coding technique in that it not only achieves channel capacity, but also does so at a faster speed of convergence than any other technique. This speed is measured by the "scaling exponent" and its importance is three-fold. Firstly, estimating the scaling exponent is challenging and demands a deeper understanding of the dynamics of communication channels. Secondly, scaling exponents serve as a benchmark for different variants of polar codes that helps us select the proper variant for real-life applications. Thirdly, the need to optimize for the scaling exponent sheds light on how to reinforce the design of polar code. In this paper, we generalize the binary erasure channel (BEC), the simplest communication channel and the protagonist of many polar code studies, to the "tetrahedral erasure channel" (TEC). We then invoke Mori-Tanaka’s 2 × 2 matrix over 𝔽_4 to construct polar codes over TEC. Our main contribution is showing that the dynamic of TECs converges to an almost-one-parameter family of channels, which then leads to an upper bound of 3.328 on the scaling exponent. This is the first non-binary matrix whose scaling exponent is upper-bounded. It also polarizes BEC faster than all known binary matrices up to 23 × 23 in size. Our result indicates that expanding the alphabet is a more effective and practical alternative to enlarging the matrix in order to achieve faster polarization.
Cite as

Iwan Duursma, Ryan Gabrys, Venkatesan Guruswami, Ting-Chun Lin, and Hsin-Po Wang. Accelerating Polarization via Alphabet Extension. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{duursma_et_al:LIPIcs.APPROX/RANDOM.2022.17,
  author =	{Duursma, Iwan and Gabrys, Ryan and Guruswami, Venkatesan and Lin, Ting-Chun and Wang, Hsin-Po},
  title =	{{Accelerating Polarization via Alphabet Extension}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.17},
  URN =		{urn:nbn:de:0030-drops-171393},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.17},
  annote =	{Keywords: polar code, scaling exponent}
}
  • Refine by Type
  • 9 Document/PDF
  • 8 Document/HTML

  • Refine by Publication Year
  • 2 2026
  • 6 2025
  • 1 2022

  • Refine by Author
  • 2 Guruswami, Venkatesan
  • 1 Bhoja, Arohee
  • 1 Codel, Cayden
  • 1 Dai, Samuel
  • 1 Dikstein, Yotam
  • Show More...

  • Refine by Series/Journal
  • 8 LIPIcs
  • 1 OASIcs

  • Refine by Classification
  • 3 Theory of computation → Error-correcting codes
  • 2 Mathematics of computing → Coding theory
  • 1 Computing methodologies → Symbolic and algebraic manipulation
  • 1 Hardware → Quantum error correction and fault tolerance
  • 1 Human-centered computing → Interaction design process and methods
  • Show More...

  • Refine by Keyword
  • 1 Algebraic geometry codes
  • 1 Cognitive load and Human Performance Issues
  • 1 Commuting Projector Code
  • 1 Extravehicular Activities
  • 1 Grassmannian expander
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact