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The undetected error probability for Reed-Solomon codes

Cheung, Kar-Ming and McEliece, Robert J. (1988) The undetected error probability for Reed-Solomon codes. In: Conference record: MILCOM 88: 21st century military communications - what's possible? IEEE , Piscataway, NJ , pp. 163-167. ISBN 70783857 http://resolver.caltech.edu/CaltechAUTHORS:20120216-080309345

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Abstract

This paper is an extension of a recent paper by McEliece and Swanson dealing with the decoder error probability for Reed-Solomon codes {more generally, linear MDS codes). McEliece and Swanson offered an upper bound on P_E(u), the decoder error probability given u symbol errors occur. In this paper, by using combinatoric technique like the principle of inclusion and exclusion, an exact formula for P_E(u) is derived. The P_E(u) of an MDS code is observed to approach Q rapidly as u gets large, where Q is the probability that a compltely random error pattern will cause decoder error. An upper bound for the expression │P_E(u)/Q-1│ is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P_E(u) indeed approaches Q as u becomes large, and some laws of large number come info play somehow.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/MILCOM.1988.13385 DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=13385PublisherUNSPECIFIED
Additional Information:© 1988 IEEE. Date of Current Version: 06 August 2002. This work was supported in part by the National Aeronautics and Space Administration under Grant NAS7-918 and in part by the Air Force Office of Scientific Research Grant AFOSR-83-0296.
Funders:
Funding AgencyGrant Number
NASANAS7-918
Air Force Office of Scientific Research (AFOSR)AFOSR-83-0296
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INSPEC Accession Number3338385
Record Number:CaltechAUTHORS:20120216-080309345
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120216-080309345
Official Citation:Kar-Ming Cheung; McEliece, R.J.; , "The undetected error probability for Reed-Solomon codes," Military Communications Conference, 1988. MILCOM 88, Conference record. '21st Century Military Communications - What's Possible?'. 1988 IEEE , vol., no., pp.163-167 vol.1, 23-26 Oct 1988 doi: 10.1109/MILCOM.1988.13385 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=13385&isnumber=552
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29326
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Feb 2012 17:23
Last Modified:26 Dec 2012 14:51

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