By Topic

Bounds on the Error Probability of Block Codes over the q-Ary Erasure Channel

Sign In

Full text access may be available.

To access full text, please use your member or institutional sign in.

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

3 Author(s)
Liva, G. ; Inst. of Commun. & Navig., Deutsches Zentrum fur Luftund Raumfahrt (DLR), Wessling, Germany ; Paolini, E. ; Chiani, M.

In this paper, tight bounds on the block error probability of linear block codes over order-q finite fields for the q-ary erasure channel, under maximum-likelihood (ML) decoding, are developed. Upper bounds are obtained for uniform parity-check ensembles, sparse parity-check ensembles, general parity-check ensembles (e.g., Gallager regular nonbinary low-density parity-check ensembles), and for any given linear code with known distance spectrum. The tightness of the upper bounds is confirmed both by the comparison with simple lower bounds and, for Gallager low-density parity-check ensembles, by extensive Monte Carlo simulations. Exploiting the derived bounds, it is shown how already for short blocks and small q>2 sparse ensembles attain block error probabilities close to those of idealized maximum distance separable (MDS) codes, down to low error probabilities, whereas in the same regime binary codes show visible losses with respect to the Singleton bound. Thanks to the accurate performance estimates, the developed bounds can support the design of near-optimum erasure correcting codes with short and moderate lengths.

Published in:

Communications, IEEE Transactions on  (Volume:61 ,  Issue: 6 )