Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

Mathieu Cunche (1) , Valentin Savin (2) , Vincent Roca (1)

1 PLANETE - Protocols and applications for the Internet
2 CEA-LETI - Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information

In this paper, we show that over the binary erasure channel, Quasi-Cyclic LDPC codes can efficiently accommodate the hybrid iterative/ML decoding. We demonstrate that the quasi- cyclic structure of the parity-check matrix can be advantageously used in order to significantly reduce the complexity of the ML decoding. This is achieved by a simple row/column permutation that transforms a QC matrix into a pseudo-band form. Based on this approach, we propose a class of QC-LDPC codes with almost ideal error correction performance under the ML decoding, while the required number of row/symbol operations scales as k √k, where k is the number of source symbols.

Mots clés: Low-density-parity-check codes; Quasi-cyclic codes; Erasure channel

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Mathieu Cunche, Valentin Savin, Vincent Roca. Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel. IEEE International Symposium on Information Theory and its Applications (ISITA 2010), Oct 2010, Taichung, Taiwan. pp.Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel. ⟨hal-00506039⟩