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 nonbinary 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. I. INTRODUCTIONDesigning codes for correcting deletions or insertions is well known to be a challenging problem; see, e.g., [1]- [8]. For the special case of correcting one insertion or deletion, there exists an elegant class of codes called Varshamov-Tenengolts (VT) codes. Binary VT codes were first introduced by Varshamov and Tenengolts in [9] for channels with asymmetric errors.Later, Levenshtein [10] showed that they can be used for correcting a single deletion or insertion with a simple decoding algorithm whose complexity is linear in the code length [1]. Tenengolts subsequently introduced a non-binary version of VT codes, defined over a q-ary alphabet for any q > 2 [11]. The q-ary VT codes retain many of the attractive properties of the binary codes. In particular, they can correct deletion or insertion of a single symbol from a q-ary VT codeword with a linear-time decoder.M. Abroshan and R. Venkataramanan are with the

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This paper considers 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.

In this paper, we consider a zero error coordination problem wherein the nodes of a network exchange messages to be able to perfectly coordinate their actions with the individual observations of each other. While previous works on coordination commonly assume an asymptotically vanishing error, we assume exact, zero error coordination. Furthermore, unlike previous works that employ the empirical or strong notions of coordination, we define and use a notion of set coordination. This notion of coordination bears similarities with the empirical notion of coordination. We observe that set coordination, in its special case of two nodes with a one-way communication link is equivalent with the "Hide and Seek" source coding problem of McEliece and Posner. The Hide and Seek problem has known intimate connections with graph entropy, rate distortion theory, Rényi mutual information and even error exponents. Other special cases of the set coordination problem relate to Witsenhausen's zero error rate and the distributed computation problem. These connections motivate a better understanding of set coordination, its connections with empirical coordination, and its study in more general setups. This paper takes a first step in this direction by proving new results for two node networks, including capacity characterizations for the linear case.

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