BCH and RS Codes for DNA Data Storage

In DNA data storage, the construction of codes and the translation of coded message symbols into physical symbols—such as the nucleotide bases A, G, C, T–are of paramount importance. In other words, the practical construction of error-correcting channel codes significantly impacts the achievement of the data durability goals set by users. In order for these codes to find application in any realistic DNA storage system, codes operating in sufficiently large field size with good distance properties must be devised. In addition, low complexity and high error-correcting designs are of significant interest to the electronic/biotechnology chip designers. This chapter concentrates on a subclass of codes, called linear codes. We will later narrow down our attention to even smaller subclasses of linear codes, called cyclic codes, subsequently Bose–Chaudhuri–Hocquenghem codes and eventually Reed-Solomon codes and cover their interesting properties that lead to practical code constructions as well as implementations that are in accordance with some of the well known DNA channels. In order for the reader to digest the material, the document will begin by giving background information about finite fields, linear spaces/subspaces through resorting to algebra fundamentals, before describing the various elegant linear code constructions based on these mathematical principles. These codes are typically used to encode raw DNA and generate protected DNA segments for more durable and reliable data storage system deployments.