| Presentation | 2023-01-24 A hierarchical construction of typical linear codes Kaito Suzuki, Tomohiko Uyematsu, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | According to Shannon's channel coding theorem, a channel has an inherent amount called a channel capacity which is determined by conditional probabilities of the channel and a probability distribution over an input alphabet. If the transmission rate is smaller than the channel capacity, there exists a pair of an encoder and a decoder of which decoding error probability vanishes as the code length tends to infinity. Further, on discrete memoryless channels, Fano and Gallager revealed that the decoding error probability decreases in an exponential function of the code length, and many researchers studied the coefficient of its exponent called reliability function. In this paper, we deal with a binary symmetric channel, and show that good linear codes can be obtained by a hierarchical construction such that bases of linear codes are selected at random and independently. The code obtained by our proposed construction achieves the error exponent of a typical random linear code given by Barg and Forney. In addition, we clarify that for an arbitrarily fixed $alpha in (0,1)$, the upper bound of the probablity to fail to construct the desired linear codes decreases in an exponential function of the $(1+alpha)$-th power of the code length, and that the coefficient of the exponent is optimum as $alpha to 1$. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | binary symmetric channel / hierarchical construction / linear code / reliability function / weight distribution |
| Paper # | IT2022-35,SIP2022-86,RCS2022-214 |
| Date of Issue | 2023-01-17 (IT, SIP, RCS) |
| Conference Information | |
| Committee | IT / RCS / SIP |
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| Conference Date | 2023/1/24(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Maebashi Terrsa |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Tetsuya Kojima(Tokyo Kosen) / Kenichi Higuchi(Tokyo Univ. of Science) / Toshihisa Tanaka(Tokyo Univ. Agri.&Tech.) |
| Vice Chair | Yasuyuki Nogami(Okayama Univ.) / Tomoya Tandai(Toshiba) / Fumihide Kojima(NICT) / Osamu Muta(Kyushu Univ.) / Koichi Ichige(Yokohama National Univ.) / Takayuki Nakachi(Ryukyu Univ.) |
| Secretary | Yasuyuki Nogami(Saitamai Univ.) / Tomoya Tandai(Nagaoka Univ. of Tech.) / Fumihide Kojima(Panasonic) / Osamu Muta(Univ. of Electro-Comm) / Koichi Ichige(Sharp) / Takayuki Nakachi(Tokyo Univ. Agri.&Tech.) |
| Assistant | Takayuki Nozaki(Yamaguchi Univ.) / Manabu Sakai(Mitsubishi Electric) / Masashi Iwabuchi(NTT) / Issei Kanno(KDDI Research) / Yuyuan Chang(Tokyo Inst. of Tech) / Kazuki Maruta(Tokyo Univ. of Science) / Taichi Yoshida(UEC) / Shoko Imaizumi(Chiba Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Information Theory / Technical Committee on Radio Communication Systems / Technical Committee on Signal Processing |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A hierarchical construction of typical linear codes |
| Sub Title (in English) | |
| Keyword(1) | binary symmetric channel |
| Keyword(2) | hierarchical construction |
| Keyword(3) | linear code |
| Keyword(4) | reliability function |
| Keyword(5) | weight distribution |
| 1st Author's Name | Kaito Suzuki |
| 1st Author's Affiliation | Tokyo Institute of Technology(Tokyo Tech.) |
| 2nd Author's Name | Tomohiko Uyematsu |
| 2nd Author's Affiliation | Tokyo Institute of Technology(Tokyo Tech.) |
| Date | 2023-01-24 |
| Paper # | IT2022-35,SIP2022-86,RCS2022-214 |
| Volume (vol) | vol.122 |
| Number (no) | IT-355,SIP-356,RCS-357 |
| Page | pp.pp.36-41(IT), pp.36-41(SIP), pp.36-41(RCS), |
| #Pages | 6 |
| Date of Issue | 2023-01-17 (IT, SIP, RCS) |