Analysis of Absorbing Sets of LDPC Codes
Lara Dolecek, Zhengya Zhang, Venkat Anantharam, Borivoje Nikolic and Martin Wainwright
Low density parity check codes (LDPC) are known to perform very well under iterative decoding in the moderate bit error rate (BER) region. However, these codes also exhibit a change in the slope of the BER vs. signal to noise ratio (SNR) curve in the very low BER region (termed error floor), a region which is of interest for many practical applications. Since this region is out of reach of pure software simulations, in general very little is known about the causes of this behavior, and consequently wider deployment of LDPC codes in such applications is still limited. We have experimentally observed that certain structures, which we call absorbing sets, intrinsic to the parity check matrix of a given code, are the dominant causes of the errors in the very low BER region. In this project we study absorbing sets of the smallest size (which are shown experimentally to dominate low BER performance) for various LDPC constructions. We have already described in detail the smallest absorbing sets for high rate array-based LDPC codes and showed how their number scales with the codeword length. By performing a comprehensive analysis of such structures, the goal is to gain a deeper understanding of why LDPC codes perform the way they do in the low BER region. This understanding will in turn lead to addressing the questions of how to design better LDPC codes (or improve existing ones) and how to analytically predict their low BER performance, both of which are presently largely unanswered.