Coding for Segmented Edit Channels.

We consider insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. No segment markers are available in the received sequence. We propose code constructions for the segmented deletion, segmented insertion, and segmented insertion-deletion channels based on subsets of Varshamov-Tenengolts codes chosen with pre-determined prefixes and/or suffixes. The proposed codes, constructed for any finite alphabet, are zero-error and can be decoded segment-by-segment. We also derive an upper bound on the rate of any zero-error code for the segmented edit channel, in terms of the segment length. This upper bound shows that the rate scaling of the proposed codes as the segment length increases is the same as that of the maximal code

Efficient Systematic Encoding of Non-binary VT Codes

Varshamov-Tenengolts (VT) codes are a class of codes which can correct a single deletion or insertion with a linear-time decoder. This paper addresses the problem of efficient encoding of non-binary VT codes, defined over an alphabet of size $q >2$. We propose a simple linear-time encoding method to systematically map binary message sequences onto VT codewords. The method provides a new lower bound on the size of $q$-ary VT codes of length $n$.Comment: This paper will appear in the proceedings of ISIT 201

Tail-Erasure-Correcting Codes

The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as a collection of two-dimensional arrays. Motivated by error patterns observed in recent prototype architectures, our study focuses on correcting erasures in the last few symbols of each row, and also correcting arbitrary deletions across rows. We present code constructions and explicit encoders and decoders that are shown to be nearly optimal in many scenarios. We show that the new coding schemes are capable of effectively mitigating these errors, making these emerging storage platforms potentially promising solutions

Coding for Segmented Edit Channels.

We consider insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. No segment markers are available in the received sequence. We propose code constructions for the segmented deletion, segmented insertion, and segmented insertion-deletion channels based on subsets of Varshamov-Tenengolts codes chosen with pre-determined prefixes and/or suffixes. The proposed codes, constructed for any finite alphabet, are zero-error and can be decoded segment-by-segment. We also derive an upper bound on the rate of any zero-error code for the segmented edit channel, in terms of the segment length. This upper bound shows that the rate scaling of the proposed codes as the segment length increases is the same as that of the maximal code