Exchange of Limits: Why Iterative Decoding Works
Abstract
We consider communication over binaryinput memoryless outputsymmetric channels using lowdensity paritycheck codes and messagepassing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of iterations is given by density evolution. Letting the number of iterations tend to infinity we get the density evolution threshold, the largest channel parameter so that the bit error probability tends to zero as a function of the iterations. In practice we often work with short codes and perform a large number of iterations. It is therefore interesting to consider what happens if in the standard analysis we exchange the order in which the blocklength and the number of iterations diverge to infinity. In particular, we can ask whether both limits give the same threshold. Although empirical observations strongly suggest that the exchange of limits is valid for all channel parameters, we limit our discussion to channel parameters below the density evolution threshold. Specifically, we show that under some suitable technical conditions the bit error probability vanishes below the density evolution threshold regardless of how the limit is taken.
 Publication:

arXiv eprints
 Pub Date:
 February 2008
 DOI:
 10.48550/arXiv.0802.1327
 arXiv:
 arXiv:0802.1327
 Bibcode:
 2008arXiv0802.1327B
 Keywords:

 Computer Science  Information Theory
 EPrint:
 16 pages