Error Floor Estimation of Long LDPC Codes on Partial Response Channels

Abstract

The presence of error floor in low density parity check (LDPC) codes is of great concern for potential applications of LDPC codes to data storage channels, which require the error correcting code (ECC) to maintain the near-capacity error correcting performance at frame error rate as low as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup> . In order to investigate the error floor of LDPC codes under partial response channels used in data storage systems, we propose a new estimation method combining analytical tools and simulation, based on the concept of trapping sets. The definition of trapping sets is based on the dominant error patterns observed in the decoding process. The goal is to accurately estimate the error rate in the error floor region for certain types of LDPC codes under the partial response channel and further extend the frame error rate down to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-14</sup> or lower. Towards this goal, we first use field programmable gate array (FPGA) hardware simulation to find the trapping sets that cause the decoding failure in the error floor region. For each trapping set, we extract the parameters which are key to the decoding failure rate caused by this trapping set. Then we use a much simpler in situ hardware simulation with these parameters to obtain the conditional decoding failure rate. By considering all the trapping sets we find, we obtain the overall frame error rate in the error floor region. The estimation results for a length -4623 QC-LDPC code under the EPR4 channel are within 0.3 dB of the direct simulation results. In addition, this method allows us to estimate the frame error rate of a LDPC code down to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-14</sup> or lower.