Log-likelihood Ratio for Low-Density Parity-Check Codes Under Binary Symmetric Erasure Channel in DNA Storage

Abstract

Due to the DNA storage system has the advantages such as high densities, longevityand efficient data duplication, more and more researchers have already focused on it. The writing/reading cost is an important indicator of the efficiency of synthesis and sequencing process. In this paper, we kept the encoding and decoding of LDPC unchanged for fair comparison. However, we propose a binary symmetric erasure channel (BSEC) model for the DNA storage system since substitution and deletion errors occurred during the synthesis and sequencing process. And then, the corresponding log-likelihood ratio (LLR) is calculated by observed error statistics under the BSEC model to achieve the lower reading cost, which is the input of the decoder for low-density parity-check (LDPC) code. Since an exact DNA channel model has not been proposed and the mismatch between the observed and theoretical error statistics, a scaling method for LLR is proposed, which can achieve a lower reading cost for DNA storage. We present the relation between total substitution and deletion error rates and scaling coefficients by curve fitting methods. From the simulation results, we can obtain that the performance of our proposed scheme is equal to or slightly better than that from the conventional scheme.