Information bits are encoded by a woven code. The woven code includes a first code, block interleaving, and a second code. The block interleaving involves row-wise writing, in a number of rows, of first code encoded bits that have been encoded by the first code, respective permutations according to which the first code encoded bits in the rows are permuted, and column-wise reading of the permuted first code encoded bits for further encoding by the second code. For rate compatibility, rate matching such as puncturing may be applied. In some embodiments, the respective permutations are based on respective prime numbers.

This disclosure describes systems and methods for detecting multiple insertion and deletion errors in the presence of substitution errors in a signal (such as a sequenced DNA string). A convolutional code that includes two or more component convolutional codes is used for encoding. Each of the two or more component convolutional codes generates only a subset of all possible outputs of the convolutional code. The subsets of the two or more component convolutional codes are disjoint from each other. Only one of the two or more convolutional codes is active at any given time. The two or more convolutional codes together define a super code. The two or more convolutional codes are time interlaced within the super code, and the super code defines the convolutional code. A trellis that includes two or more component trellises designed based on the two or more component convolutional codes is used for decoding.