Convergence analysis for a class of LDPC convolutional codes on the erasure channel

An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is introduced. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble when operating on the erasure channel is analyzed. The structured irregularity in the Tanner graph of the codes leads to significantly better thresholds when compared to the corresponding LDPC block codes.

[1]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[2]  Michael Lentmaier,et al.  To the Theory of Low-Density Convolutional Codes. II , 2001, Probl. Inf. Transm..

[3]  Daniel A. Spielman,et al.  Efficient erasure correcting codes , 2001, IEEE Trans. Inf. Theory.

[4]  Michael Lentmaier,et al.  On the Theory of Low-Density Convolutional Codes , 1999, AAECC.

[5]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[6]  Rüdiger L. Urbanke,et al.  Design of capacity-approaching irregular low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

[7]  Michael Lentmaier,et al.  An analysis of the block error probability performance of iterative decoding , 2005, IEEE Transactions on Information Theory.

[8]  R. Lathe.  Phd by thesis , 1988, Nature.

[9]  Daniel J. Costello,et al.  LDPC block and convolutional codes based on circulant matrices , 2004, IEEE Transactions on Information Theory.

[10]  K.Sh. Zigangirov,et al.  Periodic time-varying convolutional codes with low-density parity-check matrices , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[11]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[12]  Amin Shokrollahi,et al.  Capacity-achieving sequences for the erasure channel , 2002, IEEE Trans. Inf. Theory.