TS-LDPC Codes: Turbo-Structured Codes With Large Girth

We consider turbo-structured low-density parity-check (TS-LDPC) codes-structured regular codes whose Tanner graph is composed of two trees connected by an interleaver. TS-LDPC codes with good girth properties are easy to construct: careful design of the interleaver component prevents short cycles of any desired length in its Tanner graph. We present algorithms to construct TS-LDPC codes with arbitrary column weight jges2 and row weight k and arbitrary girth g. We develop a linear complexity encoding algorithm for a type of TS-LDPC codes-encoding friendly TS-LDPC (EFTS-LDPC) codes. Simulation results demonstrate that the bit-error rate (BER) performance at low signal-to-noise ratio (SNR) is competitive with the error performance of random LDPC codes of the same size, with better error floor properties at high SNR

[1]  J.M.F. Moura,et al.  Partition-and-shift LDPC codes , 2005, IEEE Transactions on Magnetics.

[2]  S. Dolinar,et al.  Weight distributions for turbo codes using random and nonrandom permutations , 1995 .

[3]  Shu Lin,et al.  Low-density parity-check codes based on finite geometries: A rediscovery and new results , 2001, IEEE Trans. Inf. Theory.

[4]  Bane V. Vasic,et al.  Structured iteratively decodable codes based on Steiner systems and their application in magnetic recording , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[5]  Urs Niesen,et al.  Grouping-and-shifting designs for structured LDPC codes with large girth , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[6]  José M. F. Moura,et al.  Turbo design for LDPC codes with large girth , 2003, 2003 4th IEEE Workshop on Signal Processing Advances in Wireless Communications - SPAWC 2003 (IEEE Cat. No.03EX689).

[7]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[8]  Ljupco Kocarev,et al.  Design of flexible-length S-random interleaver for turbo codes , 2004, IEEE Communications Letters.

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

[10]  David J. C. MacKay,et al.  Good Error-Correcting Codes Based on Very Sparse Matrices , 1997, IEEE Trans. Inf. Theory.

[11]  M. Salehi,et al.  Interleaver design for short block length turbo codes , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[12]  Robert Michael Tanner,et al.  A recursive approach to low complexity codes , 1981, IEEE Trans. Inf. Theory.

[13]  Peter J. Cameron,et al.  A brief introduction to design theory , 1975 .

[14]  David J. C. MacKay,et al.  Good Codes Based on Very Sparse Matrices , 1995, IMACC.

[15]  Li Ping,et al.  Concatenated tree codes: A low-complexity, high-performance approach , 2001, IEEE Trans. Inf. Theory.

[16]  Jin Lu,et al.  Turbo like decoding of LDPC codes , 2003, Digest of INTERMAG 2003. International Magnetics Conference (Cat. No.03CH37401).

[17]  Shu Lin,et al.  A general class of LDPC finite geometry codes and their performance , 2002, Proceedings IEEE International Symposium on Information Theory,.

[18]  R. Townsend,et al.  Self-orthogonal quasi-cyclic codes , 1967, IEEE Trans. Inf. Theory.

[19]  Shu Lin,et al.  Low density parity check codes: construction based on finite geometries , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[20]  Hatim M. Behairy,et al.  Parallel concatenated Gallager codes for CDMA applications , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[21]  J.M.F. Moura,et al.  Structured LDPC codes for high-density recording: large girth and low error floor , 2006, IEEE Transactions on Magnetics.

[22]  Evangelos Eleftheriou,et al.  Progressive edge-growth Tanner graphs , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[23]  Sarah J. Johnson,et al.  Regular low-density parity-check codes from combinatorial designs , 2001, Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494).

[24]  Sandro Bellini,et al.  Prunable S-random interleavers , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[25]  Shen Qiong-xia.  Design of Structured LDPC Codes with Large Girth , 2009 .

[26]  Bane V. Vasic,et al.  High-rate girth-eight low-density parity-check codes on rectangular integer lattices , 2004, IEEE Transactions on Communications.

[27]  Marc P. C. Fossorier,et al.  Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices , 2004, IEEE Trans. Inf. Theory.

[28]  D. Mackay,et al.  Evaluation of Gallager Codes for Short Block Length and High Rate Applications , 2001 .

[29]  J. Moura,et al.  Structured low-density parity-check codes , 2004, IEEE Signal Processing Magazine.

[30]  M. Karlin,et al.  New binary coding results by circulants , 1969, IEEE Trans. Inf. Theory.

[31]  Bane V. Vasic,et al.  Combinatorial constructions of low-density parity-check codes for iterative decoding , 2002, IEEE Transactions on Information Theory.

[32]  Sarah J. Johnson,et al.  Construction of low-density parity-check codes from Kirkman triple systems , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[33]  Jon-Lark Kim,et al.  Explicit construction of families of LDPC codes with no 4-cycles , 2004, IEEE Transactions on Information Theory.