New families of LDPC block codes formed by terminating irregular protograph-based LDPC convolutional codes

In this paper, we present a method of constructing new families of LDPC block code ensembles formed by terminating irregular protograph-based LDPC convolutional codes. Using the accumulate-repeat-by-4-jagged-accumulate (AR4JA) protograph as an example, a density evolution analysis for the binary erasure channel shows that this flexible design technique gives rise to a large selection of LDPC block code ensembles with varying code rates and thresholds close to capacity. Further, by means of an asymptotic weight enumerator analysis, we show that all the ensembles in this family also have minimum distance that grows linearly with block length, i.e., they are asymptotically good.

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

[2]  Gerhard Fettweis,et al.  Asymptotically good LDPC convolutional codes with AWGN channel thresholds close to the Shannon limit , 2010, 2010 6th International Symposium on Turbo Codes & Iterative Information Processing.

[3]  Michael Lentmaier,et al.  Distance Bounds for an Ensemble of LDPC Convolutional Codes , 2007, IEEE Transactions on Information Theory.

[4]  Rüdiger L. Urbanke,et al.  Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC , 2010, IEEE Transactions on Information Theory.

[5]  D. Costello,et al.  Approaching capacity with asymptotically regular LDPC codes , 2009, 2009 Information Theory and Applications Workshop.

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

[7]  Rudiger Urbanke,et al.  Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC , 2010, ISIT.

[8]  Gerhard Fettweis,et al.  Asymptotically regular LDPC codes with linear distance growth and thresholds close to capacity , 2010, 2010 Information Theory and Applications Workshop (ITA).

[9]  Michael Lentmaier,et al.  Convergence analysis for a class of LDPC convolutional codes on the erasure channel , 2004 .

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

[11]  Dariush Divsalar,et al.  Capacity-approaching protograph codes , 2009, IEEE Journal on Selected Areas in Communications.

[12]  Michael Lentmaier,et al.  Iterative Decoding Threshold Analysis for LDPC Convolutional Codes , 2010, IEEE Transactions on Information Theory.

[13]  Jeremy Thorpe,et al.  Enumerators for protograph ensembles of LDPC codes , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[14]  David G. M. Mitchell,et al.  Asymptotically good LDPC convolutional codes based on protographs , 2008, 2008 IEEE International Symposium on Information Theory.

[15]  J. Thorpe.  Low-Density Parity-Check (LDPC) Codes Constructed from Protographs , 2003 .

[16]  Kamil Sh. Zigangirov,et al.  Time-varying periodic convolutional codes with low-density parity-check matrix , 1999, IEEE Trans. Inf. Theory.