Pseudocodeword-free criterion for codes with cycle-free Tanner graph

  title={Pseudocodeword-free criterion for codes with cycle-free Tanner graph},
  author={Wittawat Kositwattanarerk},
  journal={Designs, Codes and Cryptography},
Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all… 



Which codes have cycle-free Tanner graphs?

It is shown that the number of cycles in a Tanner graph must increase exponentially with the length n for asymptotically good codes, and it is concluded that all binary codes that have cycle-free Tanner graphs belong to the class of graph-theoretic cut-set codes.

Selective avoidance of cycles in irregular LDPC code construction

A Viterbi-like algorithm is proposed that selectively avoids small cycle clusters that are isolated from the rest of the graph and yields codes with error floors that are orders of magnitude below those of random codes with very small degradation in capacity-approaching capability.

The effect of cycles on binary message-passing decoding of LDPC codes

  • G. Lechner
  • Computer Science
    2010 Australian Communications Theory Workshop (AusCTW)
  • 2010
We study the error-floor behavior of binary message-passing decoders for low-density parity-check (LDPC) codes. We find that the stability condition is independent of the quality of the channel

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