Concatenated tree codes: A low-complexity, high-performance approach

This paper is concerned with a family of concatenated tree (CT) codes. CT codes are special low-density parity check (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recursive/nonrecursive parts and multiple constituent codes. CT codes are decodable by the belief-propagation algorithm. They combine many advantages of LDPC and turbo codes, such as low decoding cost, fast convergence speed, and good performance.

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

[2]  Dariush Divsalar,et al.  Coding theorems for 'turbo-like' codes , 1998 .

[3]  David J. C. MacKay,et al.  Comparison of constructions of irregular Gallager codes , 1999, IEEE Trans. Commun..

[4]  Li Ping,et al.  Low density parity check codes with semi-random parity check matrix , 1999 .

[5]  Dariush Divsalar,et al.  Analysis, Design, and Iterative Decoding of Double Serially Concatenated Codes with Interleavers , 1998, IEEE J. Sel. Areas Commun..

[6]  William E. Ryan,et al.  Punctured turbo-codes for BPSK/QPSK channels , 1999, IEEE Trans. Commun..

[7]  John Cocke,et al.  Optimal decoding of linear codes for minimizing symbol error rate (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[8]  Roberto Garello,et al.  A search for good convolutional codes to be used in the construction of turbo codes , 1998, IEEE Trans. Commun..

[9]  D. Saad,et al.  Error-correcting codes that nearly saturate Shannon's bound , 1999, cond-mat/9906011.

[10]  N. Phamdo,et al.  Zigzag codes and concatenated zigzag codes , 1999, 1999 Information Theory and Networking Workshop (Cat. No.99EX371).

[11]  T. Richardson,et al.  Design of provably good low-density parity check codes , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[12]  Jung-Fu Cheng,et al.  Turbo Decoding as an Instance of Pearl's "Belief Propagation" Algorithm , 1998, IEEE J. Sel. Areas Commun..

[13]  Patrick Robertson,et al.  A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain , 1995, Proceedings IEEE International Conference on Communications ICC '95.

[14]  Hans-Andrea Loeliger,et al.  Codes and iterative decoding on general graphs , 1995, Eur. Trans. Telecommun..

[15]  Li Ping,et al.  Decoding low density parity check codes with finite quantization bits , 2000, IEEE Communications Letters.

[16]  Dariush Divsalar,et al.  Multiple turbo codes , 1995, Proceedings of MILCOM '95.

[17]  Radford M. Neal,et al.  Near Shannon limit performance of low density parity check codes , 1996 .

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

[19]  Li Ping Modified turbo codes with low decoding complexity , 1998 .

[20]  Brendan J. Frey,et al.  Iterative Decoding of Compound Codes by Probability Propagation in Graphical Models , 1998, IEEE J. Sel. Areas Commun..

[21]  Sammy Chan,et al.  Iterative decoding of multi-dimensional concatenated single parity check codes , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).

[22]  Dariush Divsalar,et al.  Soft-input soft-output modules for the construction and distributed iterative decoding of code networks , 1998, Eur. Trans. Telecommun..

[23]  Sergio Benedetto,et al.  Unveiling turbo codes: some results on parallel concatenated coding schemes , 1996, IEEE Trans. Inf. Theory.

[24]  Sae-Young Chung,et al.  On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit , 2001, IEEE Communications Letters.

[25]  M. Luby,et al.  Improved low-density parity-check codes using irregular graphs and belief propagation , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[26]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[27]  X. Jin Factor graphs and the Sum-Product Algorithm , 2002 .

[28]  C. Douillard,et al.  Multidimensional turbo codes , 1999, 1999 Information Theory and Networking Workshop (Cat. No.99EX371).