Updated on 2025/09/10

写真a

 
KASAI KENTA
 
Organization
School of Engineering Associate Professor
Title
Associate Professor
Homepage
https://kasaikenta.github.io/en.html
External link

Degree

  • 博士

Research Interests

  • quantum error correction

  • 符号理論

Research Areas

  • Informatics / Theory of informatics  / Quantum Error Correction

Research History

  • Institute of Science Tokyo   Associate Professor

    2024.10

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  • Tokyo Institute of Technology   Associate Professor

    2012.4 - 2024.9

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  • Tokyo Institute of Technology   Science of Engineering   Assistant Professor

    2009.4 - 2012.3

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  • Tokyo Institute of Technology   Science of Engineering

    2007

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  • Tokyo Institute of Technology   Science of Engineering

    2006

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Papers

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MISC

  • Performance Analysis of Spatially-Coupled MacKay-Neal Codes on Channels with Memory

    115 ( 501 )   157 - 162   2016.3

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    Language：Japanese  

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  • Spatially-Coupled Coding Approaching Symmetric Information Rate of Finite-State-Markov Fading Channels

    115 ( 396 )   267 - 271   2016.1

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    Language：Japanese  

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  • A Necessary Condition for Universally Achieving the Capacity with Spatially-Coupled Hsu-Anastasopoulos Fountain Codes

    IGARASHI Yuki, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. Information theory   114 ( 34 )   43 - 48   2014.5

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    In this report, we deal with fountain coding scheme in which a sender sends infinitely long coded bits until receivers successfully complete decoding. A fountain code is called universal if for arbitrary C∈(0,1), the code achieve any binary-input memoryless symmetric channels of capacity C. We give a necessary condition that a spatially-coupled Hsu-Anastasopoulos fountain code is universal. We numerically observe that the most efficiently decodable spatially-coupled HA fountain code satisfying the necessary condition achieves the capacity of the binary symmetric channels and binary-input additive white Gaussian noise channels by density evolution.

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  • AT-2-1 空間結合符号とその研究動向(AT-2.空間結合符号-理論限界を達成する符号-,チュートリアルセッション,ソサイエティ企画)

    笠井 健太

    電子情報通信学会総合大会講演論文集   2014   "SS - 19"-"SS-22"   2014.3

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    Language：Japanese   Publisher：一般社団法人電子情報通信学会  

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  • A Proof That Spatially-Coupled (l,3,3) MacKay-Neal Codes Achieve the Capacity of BEC

    OKAZAKI Takuya, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. Information theory   113 ( 411 )   23 - 27   2014.1

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    It was shown that spatially-coupled MacKay-Neal (MN) codes and spatially-coupled Hsu-Anastasopoulos codes achieve the capacity of the BEC by numerical experiment. Obata et al. proved that spatially-coupled (l,2,2) MN codes achieve the capacity. However, it has been observed that spatially-coupled (l,2,2) MN codes have higher error floors than spatially-coupled (l,3,3) MN codes. In this paper, we prove that spatially-coupled (l,3,3) MN codes achieve the capacity of the BEC.

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  • A Proof for Achieving the Capacity with Spatially-Coupled Hsu-Anastasopoulos Rateless Codes

    SAKATA Kosuke, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. Information theory   113 ( 411 )   29 - 34   2014.1

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    In this paper, we prove that coupled Hsu-Anastasopoulos (HA) fountain codes achieve the capacity on the BEC. In the proof, we apply the theory about potential threshold and duality of codes. As a result, we prove that coupled HA fountain codes with a bound maximum degree achieve the capacity on the BEC under BP decoding.

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  • Weight Distribution for Non-Binary Cluster LDPC Codes

    Masaki Maehara, Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    第35回 情報理論とその応用シンポジウム予稿集   abs/1305.2480   162 - 167   2012.12

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  • Stability Condition for Non-binary LDPC Codes over Galois Field

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    第35回 情報理論とその応用シンポジウム予稿集   84 - 89   2012.12

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  • Analysis of Threshold Saturation for Spatially-Coupled MacKay-Neal Codes

    OBATA Naruomi, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. Information theory   112 ( 215 )   19 - 24   2012.9

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    The belief propagation (BP) threshold of spatially-coupled (SC) low-density parity-check (LDPC) codes is equal to the MAP threshold of the underlying codes. This is called threshold saturation. Yelda et al. proved threshold saturation of SC-LDPC codes over the binary erasure channels (BEC). The approach is based on potential functions. It was observed that SC MacKay-Neal (MN) codes achieve the capacity of BEC by BP decoding. We show the potential function aproach needs a modification in the definition of energy gap. In this report, we modify the definition of energy gap and show that SC-MN codes achieve the capacity of BEC under an unproved conjecture.

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  • Efficient Termination of Spatially-Coupled Codes

    TAZOE Koji, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. Information theory   112 ( 215 )   7 - 12   2012.9

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    It has been reported that spatially-coupled Hsu-Anatasopoulos (SC-HA) codes have the bounded maximum degree and approach the Shannon limit of many channels under beleif propagation decoding. However, the encoder needs to solve large linear equations to terminate the encoding process. In this paper, we proposed modified SC-HA codes which are efficiently terminable by using an accumulator. The density evolution calculations reveal that the modified codes have higher coding rate and have the same threshold as SC-HA codes.

    DOI： 10.1109/ITW.2012.6404682

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  • Message Passing Algorithm with MAP Decoding on Zigzag Cycles for Non-binary LDPC Codes

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    IEICE Technical Report   112 ( 215 )   75 - 80   2012.9

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  • Linear Time Termination of Systematic Spatially-Coupled Codes

    TAZOE Koji, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. Information theory   112 ( 124 )   91 - 96   2012.7

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Spatially-coupled low-density parity-check codes attract much attention due to their capacity-achieving performance and the memory-efficient sliding-window decoding algorithm. On the other hand, the encoder needs to solve large linear equations to terminate the encoding process. In this paper, we propose modified spatially-coupled codes. The modified codes have less rate loss, i.e., higher coding rate, and have the same threshold as (d_l, d_r, L) codes and are efficiently terminable by using an accumulator.

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  • Optimization Method to Lower Error Floors for Generalized Non-binary LDPC Codes over Non-binary Input Memoryless Symmetric Channels

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    電子情報通信学会総合大会講演論文集   156 - 156   2012.3

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  • Quantum Error Correction Beyond the Bounded Distance Decoding Limit.

    Kenta Kasai, Manabu Hagiwara, Hideki Imai, Kohichi Sakaniwa

    IEEE Transactions on Information Theory   58 ( 2 )   1223 - 1230   2012.2

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  • Spatially-Coupled Codes for Κ-User Erasure Multiple Access Channels

    TSUJIMOTO Takayuki, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. Information theory   111 ( 390 )   7 - 12   2012.1

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    In this paper, we study low-density parity-check codes(LDPC) coded K-user erasure multiple access channels(EMAC). The support of the belief propagation message for K-user EMAC is unbounded for K≧3. We propose a reduced-complexity decoding algorithm for which only three types of messages are used and density evolution can be applied. Furthermore, we observe that significant improvement is achieved by spatially-coupled codes.

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  • Monotonicity of Error Floors for Non-binary LDPC Codes over AWGN Channels

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    電子情報通信学会総合大会講演論文集   139 - 139   2011.3

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  • Analysis of Stopping Constellation Distribution for Irregular Non-binary LDPC Code Ensemble

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    第33回 情報理論とその応用シンポジウム予稿集   94-A ( 11 )   7 - 12   2010.12

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  • Analysis of Error Floors of Non-binary LDPC Codes over q-ary Discrete Memoryless Symmetric Channel

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    第33回 情報理論とその応用シンポジウム予稿集   13 - 18   2010.12

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  • Quantum Error Correction with Non-Binary LDPC Codes

    KASAI Kenta, HAGIWARA Manabu, IMAI Hideki, SAKANIWA Koichi

    IEICE technical report   110 ( 265 )   135 - 145   2010.10

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    Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Quantum error correction is used in quantum computing and quantum communications to protect quantum information from quantum noise. Quantum LDPC codes are efficiently decodable quantum error correcting codes defined by sparse parity-check equations. CSS (Calderbank, Shor and Steane) codes are the most promising quantum error correcting codes. In this paper, we consider the quantum error correction over the depolarizing channels with non-binary LDPC codes defined over Galois field of size 2P. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., 2P, the error floors are considerably improved.

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  • Modified Cancellation for Non-binary LDPC Codes

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    電子情報通信学会総合大会講演論文集   124 - 124   2010.3

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  • Design and decoding algorithms of non-binary LDPC codes

    KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report   109 ( 328 )   43 - 49   2009.12

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    Recently, non-bibary LDPC codes over GF(2^m) attract much attention. Despite the considerable potential for error correction, non-binary LDPC codes suffer from huge decoding complexity and memory requirement. This report briefly reviews design and decoding schemes of non-binary LDPC codes.

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  • A Note on Analytical Solution of Covariance Evolution for Regular LDPC Codes

    Takayuki Nozaki, Kenta Kasai, Tomoharu Shibuya, Kohichi Sakaniwa

    IEICE Technical Report   102 ( 202 )   37 - 42   2009.9

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  • Analytical Solution of Covariance Evolution for Regular LDPC Codes

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    第31回 情報理論とその応用シンポジウム予稿集   abs/1011.1701   504 - 509   2008.10

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  • Bounds of MAP Decoding Performance for Non-binary LDPC Codes

    MUTAGUCHI Eri, KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    IEICE technical report   108 ( 202 )   31 - 36   2008.9

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Montanari constructed lower bounds on the conditional entropy of the transmitted message using Multi-Poisson ensemble. In case of BEC, this bounds are identical to the conditional entropy of the transmitted message by the analysis of EXIT function by Measson. We will consider the extention of this method to LDPC codes over GF (4).

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  • Weight Distribution of Structured LDPC Code

    KASAI Kenta

    The Brain & Neural Networks   15 ( 4 )   266 - 271   2008

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    Language：Japanese   Publisher：Japanese Neural Network Society  

    DOI： 10.3902/jnns.15.266

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  • Evolution of Degree Distribution of Residual Graphs for Detailedly Represented Irregular LDPC Code Ensembles

    Takayuki Nozaki, Kenta Kasai, Kohichi Sakaniwa

    第30回 情報理論とその応用シンポジウム予稿集   774 - 779   2007.11

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  • Minimum Distance Distributions of Irregular LDPC Code Ensembles

    MIYAMOTO Shinya, KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    29 ( 2 )   457 - 460   2006.11

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  • Multi-Edge type LDPC符号のStopping Set分布(情報通信基礎サブソサイエティ合同研究会)

    大久保達也, 笠井健太, 下山裕司, 坂庭好一

    電子情報通信学会技術研究報告. ISEC, 情報セキュリティ   105 ( 664 )   141 - 146   2006.3

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    Publisher：社団法人電子情報通信学会  

    Multi-Edge type LDPC符号(MET-LDPC符号)は,複数の正則/非正則LDPC符号をタナーグラフ上で連接させたグラフから定義されるLDPC符号である.下山らによって,MET-LDPC符号アンサンブルの平均重み分布が導出されている.本研究では,非正則LDPC符号アンサンブルが持つ,stopping set分布を得るための補助分布に関するある対称性を利用して,MET-LDPC符号アンサンプルの平均stopping set分布を導出している.

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  • 正則LDPC符号アンサンブルにおける2次のsupport weight distribution(情報通信基礎サブソサイエティ合同研究会)

    井對貴之, 笠井健太, 池谷亮志, 渋谷智治, 坂庭好一

    電子情報通信学会技術研究報告. ISEC, 情報セキュリティ   105 ( 664 )   147 - 151   2006.3

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    ある符号のsupport weight distributionは、指定した次元とsupport weightを持つユニークな部分空間の数Extrinsic information function (EXIT)関数は、support weight distributionを用いて正確に記述することができる。本稿では、正則LDPC符号アンサンブルにおける2次の平均support weight distributionを求める方法を与えている。

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  • Second Support Weight Distribution of Regular LDPC Code Ensembles

    ITSUI Takayuki, KASAI Kenta, IKEGAYA Ryoji, SHIBUYA Tomoharu, SAKANIWA Kohichi

    IEICE technical report   105 ( 662 )   147 - 151   2006.3

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    Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

    The support weight distribution of a code is the number of unique subspaces of the code with specified dimension and support weight. The extrinsic information transfer (EXIT) function on erasure channels is exactly described by the support weight distribution. In this paper, we formulate the average second support weight distribution of regular LDPC code ensembles.

    DOI： 10.1109/ISIT.2006.261666

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  • Stopping Set Distribution of Multi-Edge type LDPC Code Ensembles

    OKUBO Tatsuya, KASAI Kenta, SHIMOYAMA Yuji, SAKANIWA Kohichi

    IEICE technical report   105 ( 662 )   141 - 146   2006.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Multi-edge type LDPC (MET-LDPC) codes can be seen as beeing defined by a Tanner graph which is obtained by concatenating some Tanner graphs of irregular LDPC codes. Average codeword weight distributions of MET-LDPC code ensembles have been derived by Shimoyama et al. We find certain symmetry of multi-edge type LDPC codes with respect to their stopping set distributions. Using the symmetry, we derive the average stopping set distribution of multi-edge type LDPC code ensembles.

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  • Multi-Edge type LDPC符号のStopping Set分布(情報通信基礎サブソサイエティ合同研究会)

    大久保達也, 笠井健太, 下山裕司, 坂庭好一

    電子情報通信学会技術研究報告. WBS, ワイドバンドシステム : IEICE technical report   105 ( 666 )   141 - 146   2006.3

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    Publisher：社団法人電子情報通信学会  

    Multi-Edge type LDPC符号(MET-LDPC符号)は,複数の正則/非正則LDPC符号をタナーグラフ上で連接させたグラフから定義されるLDPC符号である.下山らによって,MET-LDPC符号アンサンブルの平均重み分布が導出されている.本研究では,非正則LDPC符号アンサンブルが持つ,stopping set分布を得るための補助分布に関するある対称性を利用して,MET-LDPC符号アンサンブルの平均stopping set分布を導出している.

    researchmap

  • 正則LDPC符号アンサンブルにおける2次のsupport weight distribution(情報通信基礎サブソサイエティ合同研究会)

    井對貴之, 笠井健太, 池谷亮志, 渋谷智治, 坂庭好一

    電子情報通信学会技術研究報告. WBS, ワイドバンドシステム : IEICE technical report   105 ( 666 )   147 - 151   2006.3

    　More details

    Publisher：社団法人電子情報通信学会  

    ある符号のsupport weight distributionは、指定した次元とsupport weightを持つユニークな部分空間の数Extrinsic information function (EXIT)関数は、support weight distributionを用いて正確に記述することができる。本稿では、正則LDPC符号アンサンプルにおける2次の平均support weight distributionを求める方法を与えている。

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  • Weight Distribution of Multi-Edge type LDPC Code Ensembles

    SHIMOYAMA Yuji, KASAI Kenta, SAKANIWA Kohichi

    28 ( 1 )   119 - 122   2005.12

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    Language：Japanese  

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  • LDPC符号のエラーフロアの解消

    市川 知行, 笠井 健太, 坂庭 好一

    電子情報通信学会技術研究報告. ISEC, 情報セキュリティ   104 ( 731 )   73 - 76   2005.3

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  • LDPC 符号のエラーフロアの解消

    市川知行, 笠井健太, 坂庭好一

    電子情報通信学会技術研究報告. ISEC, 情報セキュリティ   104 ( 731 )   73 - 76   2005.3

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    Publisher：社団法人電子情報通信学会  

    Low-Density Parity-Check(LDPC)符号の復号法として知られるBeleif Propagation(BP)は、ビット毎の最大事後確率(MAP)復号を近似する復号法である。低密度パリティ検査(LDPC)符号は、BP復号によって理論限界に近い復号性能を持つことが知られているが、そのSNR対誤り率復号性能曲線では、高いSNRで誤り率の低下が鈍るエラーフロアと呼ばれる領域が存在する。本研究の目的はこのエラーフロア領域を解消することである。エラーフロア領域において、度々復号に失敗する伝送ビットに対応するタナーグラフ上の変数ノードが成す部分グラフには、短いサイクルが存在する傾向がある。このサイクルに対して部分的なMAP復号を実現する復号アルゴリズムを提案し、エラーフロアが緩和された例を示す。

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  • Design of LDPC codes using degree distributions of Tanner graphs

    MIYAMOTO Shinya, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. WBS, Wideband System   104 ( 731 )   61 - 66   2005.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Decoding performance of LDPC (Low-Density Parity-Check) codes over a binary erasure channel (BEC) is highly dependent on the degree distributions of the Tanner graphs. We compare two types of LDPC code ensembles having uniform degree distributions and non-uniform ones respectively. Then we provide a sufficient condition for the erasure probability of a BEC for which the decoding performance for the ensembles with uniform degree distributions is superior to that with non-uniform ones.

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  • A Decoding Algorithm Lowering Error Floors of LDPC Codes

    ICHIKAWA Tomoyuki, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. WBS, Wideband System   104 ( 733 )   73 - 76   2005.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Belief Propagation decoding for Low-Density Parity-Check (LDPC) codes approximates bit-wise Maximum A posteriori Probability (MAP) decoding. LDPC codes with carefully designed degree distribution tend to have error floors in which error rate decrease slowly as SNR increases. The aim of this report is to lower error floors of LDPC codes. In error floor region, the number of error bits in decoding result blocks is small and some paticular error pertterns are frequently observed. We investigate these small errors and cycles associated with frequent error bits and present a decoding algorithm lowering error floors of LDPC codes.

    CiNii Books

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  • Design of LDPC codes using degree distributions of Tanner graphs

    MIYAMOTO Shinya, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. WBS, Wideband System   104 ( 733 )   61 - 66   2005.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Decoding performance of LDPC (Low-Density Parity-Check) codes over a binary erasure channel (BEC) is highly dependent on the degree distributions of the Tanner graphs. We compare two types of LDPC code ensembles having uniform degree distributions and non-uniform ones respectively. Then we provide a sufficient condition for the erasure probability of a BEC for which the decoding performance for the ensembles with uniform degree distributions is superior to that with non-uniform ones.

    CiNii Books

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  • LDPC 符号のエラーフロアの解消

    市川知行, 笠井健太, 坂庭好一

    電子情報通信学会技術研究報告. IT, 情報理論   104 ( 729 )   73 - 76   2005.3

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    Publisher：社団法人電子情報通信学会  

    Low-Density Parity-Check(LDPC)符号の復号法として知られるBeleif Propagation(BP)は、ビット毎の最大事後確率(MAP)復号を近似する復号法である。低密度パリティ検査(LDPC)符号は、BP復号によって理論限界に近い復号性能を持つことが知られているが、そのSNR対誤り率復号性能曲線では、高いSNRで誤り率の低下が鈍るエラーフロアと呼ばれる領域が存在する。本研究の目的はこのエラーフロア領域を解消することである。エラーフロア領域において、度々復号に失敗する伝送ビットに対応するタナーグラフ上の変数ノードが成す部分グラフには、短いサイクルが存在する傾向がある。このサイクルに対して部分的なMAP復号を実現する復号アルゴリズムを提案し、エラーフロアが緩和された例を示す。

    researchmap

  • Design of LDPC codes using degree distributions of Tanner graphs

    MIYAMOTO Shinya, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. WBS, Wideband System   104 ( 729 )   61 - 66   2005.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Decoding performance of LDPC (Low-Density Parity-Check) codes over a binary erasure channel (BEC) is highly dependent on the degree distributions of the Tanner graphs. We compare two types of LDPC code ensembles having uniform degree distributions and non-uniform ones respectively. Then we provide a sufficient condition for the erasure probability of a BEC for which the decoding performance for the ensembles with uniform degree distributions is superior to that with non-uniform ones.

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  • タナーグラフの次数分布を用いたLDPC符号の設計

    宮本 新也, 笠井 健太, 坂庭 好一

    電子情報通信学会技術研究報告. WBS, ワイドバンドシステム : IEICE technical report   104 ( 733 )   61 - 66   2005.3

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  • A Decoding Algorithm Lowering Error Floors of LDPC Codes

    ICHIKAWA Tomoyuki, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. WBS, Wideband System   104 ( 729 )   73 - 76   2005.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Belief Propagation decoding for Low-Density Parity-Check (LDPC) codes approximates bit-wise Maximum A posteriori Probability (MAP) decoding. LDPC codes with carefully designed degree distribution tend to have error floors in which error rate decrease slowly as SNR increases. The aim of this report is to lower error floors of LDPC codes. In error floor region, the number of error bits in decoding result blocks is small and some paticular error pertterns are frequently observed. We investigate these small errors and cycles associated with frequent error bits and present a decoding algorithm lowering error floors of LDPC codes.

    CiNii Books

    researchmap

  • A Decoding Algorithm Lowering Error Floors of LDPC Codes

    ICHIKAWA Tomoyuki, KASAI Kenta, SAKANIWA Kohichi

    IEICE technical report. WBS, Wideband System   104 ( 733 )   73 - 76   2005.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Belief Propagation decoding for Low-Density Parity-Check (LDPC) codes approximates bit-wise Maximum A posteriori Probability (MAP) decoding. LDPC codes with carefully designed degree distribution tend to have error floors in which error rate decrease slowly as SNR increases. The aim of this report is to lower error floors of LDPC codes. In error floor region, the number of error bits in decoding result blocks is small and some paticular error pertterns are frequently observed. We investigate these small errors and cycles associated with frequent error bits and present a decoding algorithm lowering error floors of LDPC codes.

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  • タナーグラフの次数分布を用いたLDPC符号の設計

    宮本 新也, 笠井 健太, 坂庭 好一

    電子情報通信学会技術研究報告. ISEC, 情報セキュリティ   104 ( 731 )   61 - 66   2005.3

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  • タナーグラフの次数分布を用いたLDPC符号の設計

    宮本 新也, 笠井 健太, 坂庭 好一

    電子情報通信学会技術研究報告. IT, 情報理論   104 ( 729 )   61 - 66   2005.3

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  • A Code-Equivalent Transfomation Removing Cycles of Length Four in Tanner Graphs

    KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    IEICE Tech. Rep.   104 ( 302 )   25 - 28   2004.9

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Belief Propagation(BP) decoding is equivalent to Maximum a Posteriori(MAP) decoding when the Tanner graph of the code is free of cycles. Performance of BP decoding with Tanner graph with cycle is often not good if the Tanner graph has cycles of length four. Adding redundant parity-checks and puncturing bits, Yedidia et al. transformed high-density parity-check matrices to low-density ones. In this report, we investigate the transformation of parity-check matrices (or equivalently of Tanner graphs) removing cycles of length four in Tanner graphs, which is the special case of Yedidia's transformation. We prove that, when transmission over erasure channels, under the transformation, BP-recoverable erasures are preserved. We show transforming Tanner graph of (7,4,3) Hamming code makes some new BP-recoverable erasures.

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  • Concentration of the Decoding Performance for Detailedly Represented Irregular LDPC Code Ensembles

    SHIMADA Satoshi, KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    Technical report of IEICE. ISEC   103 ( 715 )   121 - 126   2004.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Richardson et al. showed concentration of the performance of the BP decoder around its average performance in the regular and irregular LDPC code ensemble and that its average performance converges to the performance obtained by density evolution. Furthermore, Kasai et al. presented detailedly represented ensemble and its density evolution in order to look for ensembles which have better threshold than standard irregular ensembles. In this paper, we show concentration of the performance of the BP decoder around its average performance in the detailedly represented ensemble and that its average performance converges to the performance obtained by density evolution.

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  • Concentration of the Decoding Performance for Detailedly Represented Irregular LDPC Code Ensembles

    SHIMADA Satoshi, KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    Technical report of IEICE. ISEC   103 ( 713 )   121 - 126   2004.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Richardson et al. showed concentration of the performance of the BP decoder around its average performance in the regular and irregular LDPC code ensemble and that its average performance converges to the performance obtained by density evolution. Furthermore, Kasai et al. presented detailedly represented ensemble and its density evolution in order to look for ensembles which have better threshold than standard irregular ensembles. In this paper, we show concentration of the performance of the BP decoder around its average performance in the detailedly represented ensemble and that its average performance converges to the performance obtained by density evolution.

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  • Concentration of the Decoding Performance for Detailedly Represented Irregular LDPC Code Ensembles

    SHIMADA Satoshi, KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    Technical report of IEICE. ISEC   103 ( 711 )   121 - 126   2004.3

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    Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

    Richardson et al. showed concentration of the performance of the BP decoder around its average performance in the regular and irregular LDPC code ensemble and that its average performance converges to the performance obtained by density evolution. Furthermore, Kasai et al. presented detailedly represented ensemble and its density evolution in order to look for ensembles which have better threshold than standard irregular ensembles. In this paper, we show concentration of the performance of the BP decoder around its average performance in the detailedly represented ensemble and that its average performance converges to the performance obtained by density evolution.

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  • SA-5-4 Stability of Density Evolution for Detailedly Represented Irregular LDPC Codes

    Kasai Kenta, Miyakawa Satoshi, Shibuya Tomoharu, Sakaniwa Kohichi

    Proceedings of the IEICE General Conference   2004   "S - 27"   2004.3

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  • Weight Distributions of LDPC Codes with Tripartite Graphs

    SHIMOYAMA Yuji, IKEGAYA Ryoji, KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    27 ( 1 )   9 - 12   2004

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  • Asymptotic Analysis of Weight Distribution for Detailedly Represented Irregular LDPC Code Ensembles

    IKEGAYA Ryoji, KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    IEICE technical report. Information theory   103 ( 215 )   19 - 24   2003.7

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    Burshtein and Miller provided an asymptotic estimation of the exponent of the average weight distribution for conventional irregular LDPC ensembles defined by Richardson et al., which are based on bipartite graphs. This estimation is derived by the asymptotic estimation of the exponent of a coefficient in multinomials with non-negative coefficients. In this paper, we employ Burshtein's method to provide an asymptotic estimation of the exponent of the average weight distribution for detailedly represented irregular LDPC ensembles. Moreover, we present numerical examples which show the relation between the exponent of the average weight distribution for conventional and detailedly represented ensemble, and provide an example of code ensemble which has larger typical minimum distance than given conventional ensemble has.

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  • 詳細に表現された非正則LDPC符号に関する密度発展法(モバイル環境におけるPerson to person高信頼性情報流通技術)(情報通信サブソサイエティ合同研究会)

    笠井健太, 渋谷智治, 坂庭好一

    電子情報通信学会技術研究報告. ITS   102 ( 747 )   149 - 154   2003.3

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    Publisher：社団法人電子情報通信学会  

    著者らによって、低密度パリティ検査符号に関する従来のアンサンブルC(n,λ,ρ)をより詳細に表現したアンサンブルC_l(n,π)が提案され、そのアンサンブルに関する密度発展法が開発されている。しかし、その導出にはある命題の成立を仮定しており、その命題の成立は実験によって支持されているにすぎなかった。本報告では、まずより単純な命題の成立を仮定することにより、C_1(n,π)に関する従来の密度発展法が得られる事を示す。さらに、C_2(n,π)⊂C_l(n,π)なるアンサンブルC_2(n,π)を提案し、いかなる命題を仮定することなく、C_2(n,π)に関する密度発展法が得られることを示す。

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  • Density Evolution for Detailedly Represented Irregular LDPC Codes

    KASAI Kenta, SHIBUYA Tomoharu, SAKANIWA Kohichi

    Technical report of IEICE. ISEC   102 ( 743 )   149 - 154   2003.3

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    Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

    We have proposed a low-density parity-check code ensemble C_1(η,π) and developed its density evolution. The density evolution for C_1(η,π) required a conjecture which was supported empirically. In this report we simplify the conjecture to derive the density evolution for C_1(η,π). Further, we propose a subensemble C_2(η,π) ⊂ C_1(η,π) whose density evolution does not require any conjecture.

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  • 詳細に表現された非正則LDPC符号に関する密度発展法(モバイル環境におけるPerson to person高信頼性情報流通技術 : 情報通信サブソサイエティ合同研究会)

    笠井健太, 渋谷智治, 坂庭好一

    電子情報通信学会技術研究報告. SST, スペクトル拡散   102 ( 745 )   149 - 154   2003.3

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    Publisher：社団法人電子情報通信学会  

    著者らによって、低密度パリティ検査符号に関する従来のアンサンブルC(n,λ,ρ)をより詳細に表現したアンサンブルC_1(n,π)が提案され、そのアンサンブルに関する密度発展法が開発されている。しかし、その導出にはある命題の成立を仮定しており、その命題の成立は実験によって支持されているにすぎなかった。本報告では、まずより単純な命題の成立を仮定することにより、C_1(n,π)に関する従来の密度発展法が得られる事を示す。さらに、C_2(n,π)⊂C_1(n,π)なるアンサンブルC_2(n,π)を提案し、いかなる命題を仮定することなく、C_2(n,π)に関する密度発展法が得られることを示す。

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  • 詳細に表現された非正則LDPC符号に関する密度発展法(モバイル環境におけるPerson to person高信頼性情報流通技術)(情報通信サブソサイエティ合同研究会)

    笠井健太, 渋谷智治, 坂庭好一

    電子情報通信学会技術研究報告. IT, 情報理論   102 ( 741 )   149 - 154   2003.3

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    Publisher：社団法人電子情報通信学会  

    著者らによって、低密度パリティ検査符号に関する従来のアンサンブルC(η,λ,ρ)をより詳細に表現したアンサンブルC_1(η,π)が提案され、そのアンサンブルに関する密度発展法か開発されている。しかし、その導出にはある命題の成立を仮定しており、その命題の成立は実験によって支持されているにすぎなかった。本報告では、まずより単純な命題の成立を仮定することにより、C_1(η,π)に関する従来の密度発展法か得られる事を示す。さらに、C_2(η,π)⊂C_1(η,π)なるアンサンブルC_2(η,π)を提案し、いかなる命題を仮定することなく、C_2(η,π)に関する密度発展法が得られることを示す。

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