A Comparative Performance and Complexity Study of Short-Length LDPC and Turbo Product Codes

This paper presents a comparative performance and complexity study between low-density parity-check (LDPC) codes and turbo product codes (TPC) of short block length (within 2048 bits). The LDPC codes are of the semi-random (SR) type, characterized by low encoder complexity, and are further optimized by eliminating short cycles of length 4 (minimum girth 6). The TPC codes are obtained from 2D and 3D constructions chosen to match the LDPC codes' parameters. The numerical results show that the SR-LDPC codes have slightly better error performance (to within 0.5dB at a BER of 10-5 while demonstrating lower computational complexity per decoder iteration but the required number of decoding iterations is larger. However, this disadvantage is significantly reduced for moderately high signal-to-noise ratios (starting from 2.5dB). It is therefore concluded that SR-LDPC codes have a more competitive performance-complexity advantage overall

[1]  Tomoaki Ohtsuki,et al.  Low-density parity-check (LDPC) coded OFDM systems , 2001, IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211).

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

[3]  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.

[4]  Jing Li,et al.  On the performance of high-rate TPC/SPC codes and LDPC codes over partial response channels , 2002, IEEE Trans. Commun..

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

[6]  Sarah J. Johnson,et al.  A family of irregular LDPC codes with low encoding complexity , 2003, IEEE Communications Letters.

[7]  Ramesh Pyndiah,et al.  Near-optimum decoding of product codes: block turbo codes , 1998, IEEE Trans. Commun..

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

[9]  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.

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

[11]  Robert C. Williamson,et al.  Loop removal from LDPC codes , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

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