The random coding bound is tight for the average linear code

Yuval Domb; Ram Zamir; Meir Feder

doi:10.1109/EEEI.2012.6376992

The random coding bound is tight for the average linear code

Yuval Domb^*, Ram Zamir, Meir Feder

^*Corresponding author for this work

School of Electrical Engineering

Tel Aviv University

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

Abstract

In 1973, Gallager published a correspondence, consisting a proof that the random coding bound is exponentially tight for the random code ensemble at all rates, even below the expurgation rate. This result explained that the random coding upper bound does not achieve the expurgation bound due to the properties of the random ensemble, irrespective of the utilized bounding technique. It has been conjectured that this same behavior holds true, also for a random linear ensemble. This conjecture is proved in this paper. Additionally, it is shown that exponential tightness for both ensembles can be achieved by considering only the triple-wise error events.

Original language	English
Title of host publication	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
DOIs	https://doi.org/10.1109/EEEI.2012.6376992
State	Published - 2012
Event	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012 - Eilat, Israel Duration: 14 Nov 2012 → 17 Nov 2012

Publication series

Name	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012

Conference

Conference	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
Country/Territory	Israel
City	Eilat
Period	14/11/12 → 17/11/12

Access to Document

10.1109/EEEI.2012.6376992

Cite this

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title = "The random coding bound is tight for the average linear code",

abstract = "In 1973, Gallager published a correspondence, consisting a proof that the random coding bound is exponentially tight for the random code ensemble at all rates, even below the expurgation rate. This result explained that the random coding upper bound does not achieve the expurgation bound due to the properties of the random ensemble, irrespective of the utilized bounding technique. It has been conjectured that this same behavior holds true, also for a random linear ensemble. This conjecture is proved in this paper. Additionally, it is shown that exponential tightness for both ensembles can be achieved by considering only the triple-wise error events.",

author = "Yuval Domb and Ram Zamir and Meir Feder",

year = "2012",

doi = "10.1109/EEEI.2012.6376992",

language = "אנגלית",

isbn = "9781467346801",

series = "2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012",

booktitle = "2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012",

note = "2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012 ; Conference date: 14-11-2012 Through 17-11-2012",

}

Domb, Y, Zamir, R & Feder, M 2012, The random coding bound is tight for the average linear code. in 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012., 6376992, 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012, 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012, Eilat, Israel, 14/11/12. https://doi.org/10.1109/EEEI.2012.6376992

The random coding bound is tight for the average linear code. / Domb, Yuval; Zamir, Ram ; Feder, Meir.
2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012. 2012. 6376992 (2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012).

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

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The random coding bound is tight for the average linear code

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