Design of LDPC Decoders for Low Error Rate Performance
Lara Dolecek, Zhengya Zhang, Venkat Anantharam, Borivoje Nikolic and Martin Wainwright
Several high-performance low-density parity-check (LDPC) codes have parity check matrices composed of permutation submatrices. We designed a parallel-serial architecture to map the decoder of any structured LDPC code in this large family to a hardware emulation platform. Experiments in the low bit error rate (BER) region provide statistics of the error traces, which are used to investigate the causes of the error floors of the (2048,1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209,1978) array-based LDPC code. Using a low-range quantization, the error floors are dominated by the fixed-point decoding effects, which should be distinguished from errors caused by the structure of the code in a high-range implementation, termed absorbing sets [1,2]. The influence of absorbing sets can be exacerbated by quantization. In particular, quantization strongly affects which absorbing sets dominate in the error floor region. Conventional quantization schemes applied to the (2209,1978) array-based LDPC code decoder induce low-weight weak absorbing sets, and, as a result, elevate the error floor. Adaptive quantization schemes, when used in a sum-product decoder, alleviate the effects of weak absorbing sets, and only the strong ones dominate the error floor of an optimized decoder implementation . Our current work involves designing an LDPC decoder chip that demonstrates the feasibility of achieving a good low error rate performance using novel architectural and quantization choices.
- Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, and M. Wainwright, "Investigation of Error Floors of Structured Low-Density Parity-Check Codes by Hardware Emulation," Proc. IEEE GLOBECOM, San Francisco, CA, November 2006.
- L. Dolecek, Z. Zhang, V. Anantharam, M. Wainwright, and B. Nikolic, "Analysis of Absorbing Sets for Array-based LDPC Codes," Proc. IEEE Int. Conf. Communications, Glasgow, UK, June 2007.
- Z. Zhang, L. Dolecek, M. Wainwright, V. Anantharam, and B. Nikolic, "Quantization Effects of Low-Density Parity-Check Codes," Proc. IEEE Int. Conf. Communications, Glasgow, UK, June 2007.