Abstract:
Memoryless stationary channels are considered having symbols $E_1,\dots,E_M$, which are letters of the alphabet of the channel, and $M=s^k$, $s$ being a prime number and $k$ an integer. It is supposed that the symbols $E_1,\dots,E_M$ are the elements of a commutative group and, moreover, the transition probability from $E_i$ to $E_j$ coincides with the transition probability from $E_i+E_k$ to $E_j+E_k$ for all indeces $I$, $j$, $k$. It is proved that in some sense the minimum probability of errors for all the codes is asymptotically equal to the minimum probability of error for all the group codes provided the transmission rate is large enough. Some other similar results are also proved in present paper.
Citation:
R. L. Dobrushin, “The Asymptotic Optimum Properties of Group and Systematic Codes for Some Channels”, Teor. Veroyatnost. i Primenen., 8:1 (1963), 52–66; Theory Probab. Appl., 8:1 (1963), 47–60
\Bibitem{Dob63}
\by R.~L.~Dobrushin
\paper The Asymptotic Optimum Properties of Group and Systematic Codes for Some Channels
\jour Teor. Veroyatnost. i Primenen.
\yr 1963
\vol 8
\issue 1
\pages 52--66
\mathnet{http://mi.mathnet.ru/tvp4646}
\transl
\jour Theory Probab. Appl.
\yr 1963
\vol 8
\issue 1
\pages 47--60
\crossref{https://doi.org/10.1137/1108003}
Linking options:
https://www.mathnet.ru/eng/tvp4646
https://www.mathnet.ru/eng/tvp/v8/i1/p52
This publication is cited in the following 35 articles:
Ryuji Takagi, Masahito Hayashi, “When quantum memory is useful for dense coding”, Lett Math Phys, 114:3 (2024)
James Chin-Jen Pang, S. Sandeep Pradhan, Hessam Mahdavifar, 2024 IEEE International Symposium on Information Theory (ISIT), 2024, 2712
Joseph Griffin, Peihong Yuan, Petar Popovski, Ken R. Duffy, Muriel Médard, 2023 IEEE Information Theory Workshop (ITW), 2023, 341
Masahito Hayashi, Kun Wang, “Dense Coding with Locality Restriction on Decoders: Quantum Encoders versus Superquantum Encoders”, PRX Quantum, 3:3 (2022)
Alexandre Graell i Amat, Laurent Schmalen, Springer Handbooks, Springer Handbook of Optical Networks, 2020, 177
Eli Haim, Yuval Kochman, Uri Erez, “Distributed Structure: Joint Expurgation for the Multiple-Access Channel”, IEEE Trans. Inform. Theory, 63:1 (2017), 5
Song-Nam Hong, Yo-Seb Jeon, Namyoon Lee, 2017 IEEE International Conference on Communications (ICC), 2017, 1
Namyoon Lee, Song-Nam Hong, 2016 IEEE International Symposium on Information Theory (ISIT), 2016, 2359
Aria Ghasemian Sahebi, S. Sandeep Pradhan, “Abelian Group Codes for Channel Coding and Source Coding”, IEEE Trans. Inform. Theory, 61:5 (2015), 2399
Song-Nam Hong, Giuseppe Caire, “Structured Lattice Codes for Some Two-User Gaussian Networks With Cognition, Coordination, and Two Hops”, IEEE Trans. Inform. Theory, 61:5 (2015), 2624
Song-Nam Hong, Giuseppe Caire, “Compute-and-Forward Strategies for Cooperative Distributed Antenna Systems”, IEEE Trans. Inform. Theory, 59:9 (2013), 5227
Ayal Hitron, Uri Erez, 2012 IEEE International Symposium on Information Theory Proceedings, 2012, 1742
Aria G. Sahebi, S. Sandeep Pradhan, 2012 IEEE International Symposium on Information Theory Proceedings, 2012, 631
Eli Haim, Yuval Kochman, Uri Erez, 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, 2012, 1
Eli Haim, Yuval Kochman, Uri Erez, 2012 IEEE International Symposium on Information Theory Proceedings, 2012, 31
Song-Nam Hong, Giuseppe Caire, 2011 IEEE Information Theory Workshop, 2011, 420
Dinesh Krithivasan, S. Sandeep Pradhan, “Distributed Source Coding Using Abelian Group Codes: A New Achievable Rate-Distortion Region”, IEEE Trans. Inform. Theory, 57:3 (2011), 1495
Aria G. Sahebi, S. Sandeep Pradhan, 2011 IEEE International Symposium on Information Theory Proceedings, 2011, 1743
Vladimir Blinovsky, Uri Erez, Simon Litsyn, “Weight distribution moments of random linear/coset codes”, Des. Codes Cryptogr., 57:2 (2010), 127
Citation in format AMSBIB
Contact us: