By Topic

Novel Burst Error Correction Algorithms for Reed-Solomon 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

1 Author(s)

In this paper, we present three novel burst error correcting algorithms for an (n, k) Reed-Solomon code. The algorithmic complexities are of the same order as error-and-erasure decoding, O(rn), where r=n-k. In particular, their hardware implementation shares elements of Blahut error-and-erasure decoding. In contrast, all existing single-burst error correcting algorithms, which are equivalent to the proposed first algorithm, have complexity O(r2n). The first algorithm corrects the shortest single-burst with length f up to r-1. The algorithm follows the key characterization that the ending locations of all candidate bursts can be purely determined by the roots of a polynomial which is a linear function of syndromes, and moreover, the shortest burst is associated with the longest sequence of consecutive roots. The algorithmic miscorrection probability is bounded by q-(r-1-f), where q denotes the field size. The second algorithm extends the first one to correct the shortest burst with length fr-3 and additionally a random symbol error. The algorithmic miscorrection probability is bounded by q-(r-3-f). The third algorithm probabilistically corrects the shortest burst with length fr-1-2δ and additionally δ (a small constant) random symbol errors. The algorithmic miscorrection and failure probabilities are both bounded by q-(r-1-2δ-f). Our simulation results for (60, 40) and (30, 16) shortened Reed-Solomon codes verify that the miscorrection probability for three algorithms and the failure probability for the third algorithm all decay exponentially (at the rate of q-1) with respect to the length of burst.

Published in:

Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 2 )