We report on coding methods for efficiently synthesizing deoxyribonucleic acid (DNA) for massive data storage, where a plurality of DNA strands are synthesized in parallel. We examine the trade-offs between the information contents, redundancy, and the average or maximum number of cycles required for synthesizing a plurality of parallel DNA strands. We analyze coding methods such as guided scrambling and constrained codes for minimizing the cycle count.@en

Decoders minimizing the Euclidean distance between the received word and the candidate codewords are known to be optimal for channels suffering from Gaussian noise. However, when the stored or transmitted signals are also corrupted by an unknown offset, other decoders may perform better. In particular, applying the Euclidean distance on normalized words makes the decoding result independent of the offset. The use of this distance measure calls for alternative code design criteria in order to get good performance in the presence of both noise and offset. In this context, various adapted versions of classical binary block codes are proposed, such as (i) cosets of linear codes, (ii) (unions of) constant weight codes, and (iii) unordered codes. It is shown that considerable performance improvements can be achieved, particularly when the offset is large compared to the noise.

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We consider the transmission and storage of encoded strings of symbols over a noisy channel, where dynamic threshold detection is proposed for achieving resilience against unknown scaling and offset of the received signal. We derive simple rules for dynamically estimating the unknown scale (gain) and offset. The estimates of the actual gain and offset so obtained are used to adjust the threshold levels or to re-scale the received signal within its regular range. Then, the re-scaled signal, brought into its standard range, can be forwarded to the final detection/decoding system, where optimum use can be made of the distance properties of the code by applying, for example, the Chase algorithm. A worked example of a spin-torque transfer magnetic random access memory (STT-MRAM) with an application to an extended (72, 64) Hamming code is described, where the retrieved signal is perturbed by additive Gaussian noise and unknown gain or offset.

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