BIC Codes: Bit Insertion-Based Constrained Codes With Error Correction for DNA Storage

Abstract

In this article, we propose a new coding algorithm for DNA storage over both error-free and error channels. For the error-free case, we propose a constrained code called bit insertion-based constrained (BIC) code. BIC codes convert a binary data sequence to multiple oligo sequences satisfying the maximum homopolymer run (i.e., run-length (RL)) constraint by inserting dummy bits. We show that the BIC codes nearly achieves the capacity in terms of information density while the simple structure of the BIC codes allows linear-time encoding and fast parallel decoding. Also, by combining a balancing technique with the BIC codes, we obtain the constrained coding algorithm to satisfy the GC-content constraint as well as the RL constraint. Next, for DNA storage channel with errors, we integrate the proposed constrained coding algorithm with a rate-compatible low-density parity-check (LDPC) code to correct errors and erasures. Specifically, we incorporate LDPC codes adopted in the 5 G new radio standard because they have powerful error-correction capability and appealing features for the integration. Simulation results show that the proposed integrated coding algorithm outperforms existing coding algorithms in terms of information density and error correctability.