Design of LDPC Decoders for Low Error Rate Performance
Zhengya Zhang, Pamela Lee, Lara Dolecek1, Borivoje Nikolic, Venkat Anantharam and Martin Wainwright
National Science Foundation CCF-0635372, Marvell, Intel, Infineon Technologies and UC MICRO
Low-density parity-check (LDPC) codes have been demonstrated to perform very close to the Shannon limit when decoded iteratively. Sometimes excellent performance is only observed up until a moderate bit error rate (BER); at a lower BER, the error curve often changes its slope, manifesting a so-called error floor. Such error floors are a major factor in limiting the deployment of LDPC codes in high-throughput applications.
We design a parallel-serial architecture to map the decoders of structured LDPC codes to a hardware emulation platform. Experiments in the low BER region provide statistics of the error traces, which are used to investigate the causes of the error floors . Different classes of errors cause error floors. But even with an optimal implementation, the error floors are inevitable due to certain combinatorial structures of the LDPC code, termed absorbing sets . The effect of absorbing sets in determining the error floor level is influenced by implementation. Conventional decoder implementations tend to induce low-weight weak absorbing sets, and, as a result, elevate the error floor. We propose alternative quantization schemes and demonstrate seemingly inferior algorithms that alleviate the effects of weak absorbing sets . Furthermore, we can exploit the structure of absorbing sets with a redesigned message-passing decoder to escape such local minimum states . The investigative approach and ASIC design approach are unified using a Simulink-based design flow. Rapid prototyping allows us to concurrently explore the algorithmic, architectural, and implementation spaces in order to optimize the decoder design.
- Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, and M. Wainwright, "GEN03-6: Investigation of Error Floors of Structured Low-Density Parity-Check Codes by Hardware Emulation," IEEE GLOBECOM Global Telecommunications Conference, November 2006, pp. 1-6.
- L. Dolecek, Z. Zhang, V. Anantharam, M. Wainwright, and B. Nikolic, "Analysis of Absorbing Sets for Array-based LDPC Codes," IEEE International Conference on Communications, June 2007, pp. 6261-6268.
- Z. Zhang, L. Dolecek, M. Wainwright, V. Anantharam, and B. Nikolic, "Quantization Effects in Low-Density Parity-Check Decoders," IEEE International Conference on Communications, June 2007, pp. 6231-6237.
- Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, and M. J. Wainwright, "Lowering LDPC Error Floors by Postprocessing," Proc. IEEE GLOBECOM, New Orleans, LA, November 2008.
- P. Lee, L. Dolecek, Z. Zhang, V. Anantharam, B. Nikolic, and M. J. Wainwright, "Error Floors in LDPC Codes: Fast Simulation, Bounds, and Hardware Emulation," ISIT International Symposium on Information Theory, July 2008, pp. 444-448.
1Massachusetts Institute of Technology