Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain

Jossy Sayir

Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain

Information Theory 2014-07-22 v2 math.IT

Authors: Jossy Sayir

Abstract

The Extended Min-Sum (EMS) algorithm for non-binary low-density parity-check (LDPC) defined over an alphabet of size $q$ operates on truncated messages of length $q'$ to achieve a complexity of the order $q'^2$ . In contrast, Walsh-Hadamard (WH) transform based iterative decoders achieve a complexity of the order $q\log q$ , which is much larger for $q'<<q$ . In this paper, we demonstrate that considerable savings can be achieved by letting WH based decoders operate on truncated messages as well. We concentrate on the direct WH transform and compute the number of operations required if only $q'$ of the $q$ inputs are non-zero. Our paper does not cover the inverse WH transform and hence further research is needed to construct WH based decoders that can compete with the EMS algorithm on complexity terms.

Keywords

low-density parity-check codes decoding algorithm

Cite

@article{arxiv.1407.4342,
  title  = {Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain},
  author = {Jossy Sayir},
  journal= {arXiv preprint arXiv:1407.4342},
  year   = {2014}
}

Comments

5 pages, accepted for publication at the International Symposium on Information Theory and its Applications (ISITA 2014), October 2014

Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain

Abstract

Keywords

Cite

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