Figure 6.

Inner–Outer Code. Encoding. The original information is first encoded with an outer code that introduces redundancy and protects against the loss of sequences. In Grass et al.⁴ the original information was first grouped into blocks of multiple sequences (light blue). Then, each row was encoded with a Reed–Solomon code that adds redundancy (yellow). The columns correspond to single DNA sequences. These are labeled with a unique index (purple). Each column is then encoded with an inner code that adds logical redundancy on the level of each sequence (green). In general, the inner and outer codes need not add the redundancy separate from the original data, but instead return a modified longer word. Decoding. The original information from the set of noisy sequences (errors marked in red) is retrieved by first decoding the inner code. This removes most errors within the sequences. For large error rates dominated by insertions and deletions, this step may be preceded by a clustering and alignment step that generates sequences with fewer errors from multiple noisy copies. The sequences are ordered by their index. The ordered sequences are then decoded by the outer code. Here, lost sequences correspond to erasures and erroneous sequences to substitutions. These are corrected by the outer code.