An improved low-complexity sum-product decoding algorithm for low-density parity-check codes

Abstract

In this paper, an improved low-complexity sum-product decoding algorithm is presented for low-density parity-check (LDPC) codes. In the proposed algorithm, reduction in computational complexity is achieved by utilizing fast Fourier transform (FFT) with time shift in the check node process. The improvement in the decoding performance is achieved by utilizing an optimized integer constant in the variable node process. Simulation results show that the proposed algorithm achieves an overall coding gain improvement ranging from 0.04 to 0.46 dB. Moreover, when compared with the sum-product algorithm (SPA), the proposed decoding algorithm can achieve a reduction of 42%-67% of the total number of arithmetic operations required for the decoding process.

Keywords

Computational complexity / Coding gain / Fast Fourier transform (FFT) / Low-density parity-check (LDPC) codes / Sum-product algorithm (SPA)

References

[1] Chandrasetty, V.A., Aziz, S.M., 2011. FPGA implementation of a LDPC decoder using a reduced complexity message passing algorithm. J. Netw., 6(1): 36-45. [

[2] Chung, S.Y., Forney, G.D., Richardson, T.J., , 2001. On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Commun. Lett., 5(2): 58-60. [

[3] Fossorier, M.P.C., Mihaljevic, M., Imai, H., 1999. Reduced complexity iterative decoding of low-density parity check codes based on belief propagation. IEEE Trans. Commun., 47(5): 673-680. [

[4] Gallager, R.G., 1962. Low-density parity-check codes. IRE Trans. Inform. Theory, 8(1): 21-28. [

[5] Goupil, A., Colas, M., Gelle, G., , 2007. FFT-based BP decoding of general LDPC codes over Abelian groups. IEEE Trans. Commun., 55(4): 644-649. [

[6] He, Y.C., Sun, S.H., Wang, X.M., 2002. Fast decoding of LDPC codes using quantisation. Electron. Lett., 38(4): 189-190. [

[7] IEEE, 2009. IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Broadband Wireless Access Systems. IEEE Std 802.16-2009. [

[8] IEEE, 2015. IEEE Draft Standard for Information Technology—Telecommunications and Information Exchange Between Systems Local and Metropolitan Area Networks—Specific Requirements Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications. IEEE P802.11-REVmc/D4.0.

[9] Jiang, X., Lee, M.H., Qi, J., 2012. Improved progressive edge-growth algorithm for fast encodable LDPC codes. EURASIP J. Wirel. Commun. Netw., 2012: 178.1-178.10. [

[10] Johnson, S.G., Frigo, M., 2007. A modified split-radix FFT with fewer arithmetic operations. IEEE Trans. Signal Process., 55(1): 111-119. [

[11] Lee, M.H., Han, J.H., Sunwoo, M.H., 2008. New simplified sum-product algorithm for low complexity LDPC decoding. IEEE Workshop on Signal Processing Systems, p.61-66. [

[12] MacKay, D.J.C., Neal, R.M., 1997. Near Shannon limit performance of low density parity check codes. Electron. Lett., 33(6): 457-458. [

[13] Morello, A., Mignone, V., 2006. DVB-S2: the second generation standard for satellite broad-band services. Proc. IEEE, 94(1): 210-227. [

[14] Papaharalabos, S., Sweeney, P., Evans, B.G., , 2007. Modified sum-product algorithm for decoding lowdensity parity-check codes. IET Commun., 1(3): 294-300. [

[15] Richardson, T.J., Urbanke, R.L., 2001. The capacity of lowdensity parity-check codes under message-passing decoding. IEEE Trans. Inform. Theory, 47(2): 599-618. [

[16] Safarnejad, L., Sadeghi, M.R., 2012. FFT based sum-product algorithm for decoding LDPC lattices. IEEE Commun. Lett., 16(9): 1504-1507. [

[17] Sorensen, H.V., Heideman, M., Burrus, C.S., 1986. On computing the split-radix FFT. IEEE Trans. Acoust. Speech Signal Process., 34(1): 152-156. [

[18] Yuan, L., Tian, X., Chen, Y., 2011. Pruning split-radix FFT with time shift. Proc. Int. Conf. on Electronics, Communications and Control, p.1581-1586. [