Cart (Loading....) | Create Account
Close category search window
 

Soft Decoding, Dual BCH Codes, and Better List-Decodable \varepsilon -Biased Codes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Guruswami, V. ; Comput. Sci. Dept., Carnegie Mellon Univ., Pittsburgh, PA, USA ; Rudra, A.

Explicit constructions of binary linear codes that are efficiently list-decodable up to a fraction (1/2 - ε) of errors are given. The codes encode k bits into n = poly(k/ε) bits and are constructible and list-decodable in time polynomial in k and 1/ε (in particular, ε need not be constant and can even be polynomially small in n). These results give the best known polynomial dependence of n on k and 1/ε for such codes. Specifically, they are able to achieve n ≤ Õ(k33+γ) or, if a linear dependence on k is required, n ≤ O(k/ε5+γ) , where γ >; 0 is an arbitrary constant. The best previously known constructive bounds in this setting were n ≤ O(k24) and n ≤ O(k/ε6) . Nonconstructively, a random linear encoding of length n = O(k/ε2) suffices, but no subexponential algorithm is known for list decoding random codes. In addition to being a basic question in coding theory, codes that are list-decodable from a fraction (1/2 - ε) of errors for ε → 0 are important in several complexity theory applications. For example, the construction with near-cubic dependence on ε yields better hardness results for the problem of approximating NP witnesses. Further, the codes constructed have the property that all nonzero codewords have relative Hamming weights in the range (1/2 - ε, 1/2 + ε); this ε-biased property is a fundamental notion in pseudorandomness.

Published in:

Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 2 )

Date of Publication:

Feb. 2011

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.