Distance preserving maps and combinatorial joint source-channel coding for large alphabets

Arya Mazumdar; Yury Polyanskiy; Ankit Singh Rawat; Hajir Roozbehani

doi:10.1109/ISIT.2016.7541863

Distance preserving maps and combinatorial joint source-channel coding for large alphabets

Arya Mazumdar
, Yury Polyanskiy
, Ankit Singh Rawat
, Hajir Roozbehani

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

In this paper we present several results regarding distance preserving maps between nonbinary Hamming spaces and combinatorial (adversarial) joint source-channel coding. In an (α, β)-map from one Hamming space to another, any two sequences that are at least α relative distance apart, are mapped to sequences that are relative distance at least β apart. The motivation to study such maps come from (D, δ)-joint source-channel coding (JSCC) schemes, where any encoded sequence must be recovered within a relative distortion D, even in the presence of δ proportion of adversarial errors. We provide bounds on the parameters of both (α, β)-maps and (D,δ)-JSCC for nonbinary alphabets. We also provide constructive schemes for both, that are optimal for many cases.

Original language	English (US)
Title of host publication	Proceedings - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3067-3071
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541863
State	Published - Aug 10 2016
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: Jul 10 2016 → Jul 15 2016

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2016-August
ISSN (Electronic)	2157-8117

Other

Other	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/Territory	Spain
City	Barcelona
Period	7/10/16 → 7/15/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Publisher link

10.1109/ISIT.2016.7541863

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Mazumdar, A., Polyanskiy, Y., Rawat, A. S., & Roozbehani, H. (2016). Distance preserving maps and combinatorial joint source-channel coding for large alphabets. In Proceedings - 2016 IEEE International Symposium on Information Theory, ISIT 2016 (pp. 3067-3071). Article 7541863 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541863

Distance preserving maps and combinatorial joint source-channel coding for large alphabets. / Mazumdar, Arya; Polyanskiy, Yury; Rawat, Ankit Singh et al.
Proceedings - 2016 IEEE International Symposium on Information Theory, ISIT 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 3067-3071 7541863 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Mazumdar, A, Polyanskiy, Y, Rawat, AS & Roozbehani, H 2016, Distance preserving maps and combinatorial joint source-channel coding for large alphabets. in Proceedings - 2016 IEEE International Symposium on Information Theory, ISIT 2016., 7541863, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers Inc., pp. 3067-3071, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 7/10/16. https://doi.org/10.1109/ISIT.2016.7541863

Mazumdar A, Polyanskiy Y, Rawat AS, Roozbehani H. Distance preserving maps and combinatorial joint source-channel coding for large alphabets. In Proceedings - 2016 IEEE International Symposium on Information Theory, ISIT 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 3067-3071. 7541863. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2016.7541863

Mazumdar, Arya ; Polyanskiy, Yury ; Rawat, Ankit Singh et al. / Distance preserving maps and combinatorial joint source-channel coding for large alphabets. Proceedings - 2016 IEEE International Symposium on Information Theory, ISIT 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 3067-3071 (IEEE International Symposium on Information Theory - Proceedings).

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abstract = "In this paper we present several results regarding distance preserving maps between nonbinary Hamming spaces and combinatorial (adversarial) joint source-channel coding. In an (α, β)-map from one Hamming space to another, any two sequences that are at least α relative distance apart, are mapped to sequences that are relative distance at least β apart. The motivation to study such maps come from (D, δ)-joint source-channel coding (JSCC) schemes, where any encoded sequence must be recovered within a relative distortion D, even in the presence of δ proportion of adversarial errors. We provide bounds on the parameters of both (α, β)-maps and (D,δ)-JSCC for nonbinary alphabets. We also provide constructive schemes for both, that are optimal for many cases.",

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Distance preserving maps and combinatorial joint source-channel coding for large alphabets

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