Density Evolution for the Design of Non-Binary Low Density Parity Check Codes for Slepian-Wolf Coding

Elsa Dupraz (1) , Valentin Savin (2) , Michel Kieffer (1, 3, 4)

1 L2S - Laboratoire des signaux et systèmes
2 CEA-LETI - Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information
3 LTCI - Laboratoire Traitement et Communication de l'Information
4 IUF - Institut universitaire de France

In this paper, we investigate the problem of designing good non-binary LDPC codes for Slepian-Wolf coding. The design method is based on Density Evolution which gives the asymptotic error probability of the decoder for given code degree distributions. Density Evolution was originally introduced for channel coding under the assumption that the channel is symmetric. In Slepian-Wolf coding, the correlation channel is not necessarily symmetric and the source distribution has to be taken into account. In this paper, we express the non-binary Density Evolution recursion for Slepian-Wolf coding. From Density Evolution, we then perform code degree distribution optimization using an optimization algorithm called differential evolution. Both asymptotic performance evaluation and finite-length simulations show the gain at considering optimized degree distributions for SW coding.

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]

Elsa Dupraz, Valentin Savin, Michel Kieffer. Density Evolution for the Design of Non-Binary Low Density Parity Check Codes for Slepian-Wolf Coding. IEEE Transactions on Communications, 2015, 63 (1), pp.25-36. ⟨10.1109/TCOMM.2014.2382126⟩. ⟨hal-01259462⟩