Efficient VLSI architecture for interpolation decoding of hermitian codes

Srivastava, Shraddha,Kwankyu Lee,Popovici, Emanuel IET 2014 IET COMMUNICATIONS Vol.8 No.5

<P>A fast, area efficient very large scale integration (VLSI) architecture is proposed for a unique decoding algorithm of Hermitian codes which was presented recently by Lee and O'Sullivan from an interpolation perspective. The algorithm iteratively computes the sent message through a majority voting procedure by using the Gröbner bases of interpolation modules. The algorithm has a regular structure which makes it suitable for VLSI implementation. The circuitry is simplified as the decoding algorithm directly gives the message word at the end of the decoding algorithm without separate steps like Chien search and Forney's formula. In terms of hardware requirements, for the widely used high rate Hermitian codes, the Lee-O'Sullivan algorithm is <I>q</I> times faster than Kötters algorithm with the same space complexity of <I>O</I>(<I>q</I><SUP>4</SUP>). Further speed improvements can be achieved by combining the main idea of Guruswami list decoding with the Lee-O'Sullivan algorithm. In terms of hardware, the addition of this concept, will further reduce the running time of the algorithm and make the circuitry about two times faster than the original Lee-O'Sullivan algorithm. The implementation results for both the Köetter and the Lee-O'Sullivan algorithms on Xilinx Virtex-5 shows that the proposed decoder can be operated at higher clock frequency with almost same area complexity.</P>

Fast Unique Decoding of Plane AG Codes

( Kwankyu Lee ) 호남수학회 2013 호남수학학술지 Vol.35 No.4

An interpolation-based unique decoding algorithm of Algebraic Geometry codes was recently introduced. The algorithm iteratively computes the sent message through a majority voting procedure using the Grobner bases of interpolation modules. We now combine the main idea of the Guruswami-Sudan list decoding with the algorithm, and thus obtain a hybrid unique decoding algorithm of plane AG codes, significantly improving the decoding speed.

FAST UNIQUE DECODING OF PLANE AG CODES

Lee, Kwankyu The Honam Mathematical Society 2013 호남수학학술지 Vol.35 No.4

An interpolation-based unique decoding algorithm of Algebraic Geometry codes was recently introduced. The algorithm iteratively computes the sent message through a majority voting procedure using the Gr$\ddot{o}$bner bases of interpolation modules. We now combine the main idea of the Guruswami-Sudan list decoding with the algorithm, and thus obtain a hybrid unique decoding algorithm of plane AG codes, significantly improving the decoding speed.

List decoding of Hermitian codes using Gröbner bases

Lee, Kwankyu,O’Sullivan, Michael E. Elsevier 2009 Journal of symbolic computation Vol.44 No.12

<P><B>Abstract</B></P><P>List decoding of Hermitian codes is reformulated to yield an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Gröbner bases of modules. The computational complexity of the algorithm seems comparable to previously known algorithms achieving the same task, and the algorithm is better suited for hardware implementation.</P>

UNIQUE DECODING OF PLANE AG CODES REVISITED

Lee, Kwankyu The Korean Society for Computational and Applied M 2014 Journal of applied mathematics & informatics Vol.32 No.1

We reformulate an interpolation-based unique decoding algorithm of AG codes, using the theory of Gr$\ddot{o}$bner bases of modules on the coordinate ring of the base curve. The conceptual description of the reformulated algorithm lets us better understand the majority voting procedure, which is central in the interpolation-based unique decoding. Moreover the smaller Gr$\ddot{o}$bner bases imply smaller space and time complexity of the algorithm.

Unique Decoding of Plane AG Codes via Interpolation

Kwankyu Lee,Bras-Amoros, M.,O'Sullivan, M. E. IEEE 2012 IEEE transactions on information theory Vol.58 No.6

<P>We present a unique decoding algorithm of algebraic geometry (AG) codes on plane curves, Hermitian codes in particular, from an interpolation point of view. The algorithm successfully corrects errors of weight up to half of the order bound on the minimum distance of the AG code. It is the first decoding algorithm to combine some features of the interpolation-based list decoding with the performance of the syndrome decoding with the majority voting scheme. The regular structure of the algorithm allows a straightforward parallel implementation.</P>

GROUP OF POLYNOMIAL PERMUTATIONS OF ℤ_p_r

Lee, Kwankyu,Lee, Heisook The Honam Mathematical Society 2012 호남수학학술지 Vol.34 No.4

The set of all polynomial permutations of $\mathbb{Z}_{p^r}$ forms a group. We investigate the structure of the group and some related groups, and completely determine the structure of the group of all polynomial permutations of $\mathbb{Z}_{p^2}$.

A COMPLEXITY-REDUCED INTERPOLATION ALGORITHM FOR SOFT-DECISION DECODING OF REED-SOLOMON CODES

Lee, Kwankyu The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.5

Soon after Lee and O'Sullivan proposed a new interpolation algorithm for algebraic soft-decision decoding of Reed-Solomon codes, there have been some attempts to apply a coordinate transformation technique to the new algorithm, with a remarkable complexity reducing effect. In this paper, a conceptually simple way of applying the transformation technique to the interpolation algorithm is proposed.

경험적 대기능의 장르별 실현 양상 비교 연구 ― 초등학교 5학년 학습자 텍스트를 중심으로

이관규 ( Lee Kwankyu ),정혜현 ( Jeong Hyehyeon ),노하늘 ( Noh Haneul ),신희성 ( Shin Heeseong ) 국어교육학회 2021 國語敎育學硏究 Vol.56 No.1

본 연구에서는 체계기능언어학 이론을 활용해 초등학생의 글에서 경험적 대기능의 실현이 장르에 따라 어떤 차이를 보이는지 살피고자 했다. 언어가 가진 여러 기능 중 경험적 대기능은 인간의 경험을 언어로 표상해 내는 방식에 초점을 둔다. 인간의 다양한 경험은 역시나 다양한 언어로 나타나며 또 동일한 경험도 다른 언어로 실현될 수 있다. 경험적 대기능을 적절히 조절하는 능력은 주체적인 언어 사용에 중요한 요인 중 하나가 될 수 있다. 또한 최근 장르 개념이 국어교육의 내용을 조직하는 데 있어 다양하게 역할하고 있는바, 실제 학습자의 언어가 장르에 따라 다른 양상을 보이는지 확인할 필요가 있었다. 본 연구는 학령기 학습자 중 초등학교 5학년을 대상으로 설명하는 글, 주장하는 글, 정서를 표현하는 글을 수집하였으며, 이를 동성 프로파일링 절차에 따라 분석하였다. 동성 프로파일링 절차에 따라 과정 유형 및 참여자 구성 패턴의 빈도를 산출할 수 있었으며 여기에 설명하는 글, 주장하는 글, 정서를 표현하는 글을 주요 변수로 두고 통계적 검증을 실시하였다. 그 결과 9개 과정 중 6개 과정에서, 74가지 참여자 구성 패턴 중 17가지에서 유의한 차이를 확인할 수 있었다. 이러한 차이들은 다시 질적인 해석을 필요로 하는데 본 연구에서는 동일하게 발화적 과정을 선택하면서도 설명하는 글과 정서를 표현하는 글의 참여자 유형 패턴에 유의한 차이가 있음에 주목하였다. 설명하는 글에서는 정서를 표현하는 글에 비해 발화자를 문면에 내세우지 않고 또 투사를 통해 직접 인용하기보다 발화 내용을 명사화하는 경향이 나타났다. 이는 정서를 표현하는 글을 보다 생동감 있게 표현하려는 필자의 의식이 발현된 것으로 볼 여지가 있다. 앞으로 다른 학령기 학습자에게서는 장르 변인이 경험적 대기능 실현 양상에 어떤 영향을 미치는지에 대한 연구와 초등학교 5학년의 언어적 선택에 작용한 기제를 질적으로 해석하는 연구가 이어질 필요가 있다 This study aims to explore how the realization of experiential metafunction varies depending on the genre in elementary school students' writing. Among the various functions of language, experiential metafunction focuses on the way human experience is represented in language. Various human experiences appear in different lexicogrammars; however, the same experience can also be realized in different lexicogrammars. The ability to properly regulate experiential metafunction can be one of the key factors in subjective language use. In addition, it was necessary to check whether the language of actual learners varies depending on the genre, as the genre concept has recently played a diverse role in organizing the contents of Korean language education system. We collected sample writings of explanations, arguments, and emotional expressions among school-age learners from fifth graders in elementary school, and analyzed them according to the transitivity profiling procedure, which allowed us to calculate the frequency of process types and participant type patterns. Statistical validation was conducted with genre as the main variables. As a result, in six of the nine process types, 17 of the 74 participant type patterns were able to identify significant differences. These differences require additional qualitative interpretation. In this work, we note that there are significant differences in the participant type patterns of writing explanations and emotional expressions while equally choosing the verbal process. In the explaining writing, the sayer was not realized as much as in the writing expressing emotions, and there was a tendency to nominalize the speech content rather than direct citation through projections. In the future, other school-age learners studies should explore how genre variations affect the realization of experiential metafunction and qualitatively interpret the mechanisms that influence the linguistic choices of fifth graders.

남북한 어문 규범의 사잇소리 표기법과 발음법에 대한 비교 연구

이관규 ( Lee Kwankyu ) 한국문법교육학회 2016 문법 교육 Vol.28 No.-

The purposes of this paper are to compare orthography and phonetic rules of Sai-sori (SA) within the language norms between South and North Korea, and to seek the unified orthography and phonetic rules of SA. Because the two Koreas` language norms are historically based on `Hangeul Orthography Unification`(1933), similarities on the orthography of SA are found. The basic principles are rooted upon the formalized orthography theory, and both nations recognize the phonetic rules of SA. Also, `ㄷ` or [t] and `ㄴ` or [n] sounds are admitted to have a common as specified SAs as well as `ㅂ` or [b] and `ㅎ` or [h] as historical SAs. However, a few differences are also detected. South Korea uses Saisios (`ㅅ`) while North Korea does not. In addition, South Korea marks the historical `ㅎ` or [h] as they utilize the words, `수캐` and `암퇘지`. On the other hand, North Korea dismisses the usages of `ㅎ` as they mark the words, `수개` and `암돼지`. South Korea only applies `ㅅ` in 6 Chinese words, but North Korea`s language does not contain a single usage of `ㅅ`. I suggest that Saisios can be omitted in the future unified Korea. It means that the formalism idea is sustained and preserved well. It would become simpler to indicate any SA expressions in dictionaries with phonetic marks. The rule could be applied to the native tongue or Chinese Korean words.