Security Enhanced Symmetric Key Encryption Employing an Integer Code for the Erasure Channel

An instance of the framework for cryptographic security enhancement of symmetric-key encryption employing a dedicated error correction encoding is addressed. The main components of the proposal are: (i) a dedicated error correction coding and (ii) the use of a dedicated simulator of the noisy channel. The proposed error correction coding is designed for the binary erasure channel where at most one bit is erased in each codeword byte. The proposed encryption has been evaluated in the traditional scenario where we consider the advantage of an attacker to correctly decide to which of two known messages the given ciphertext corresponds. The evaluation shows that the proposed encryption provides a reduction of the considered attacker’s advantage in comparison with the initial encryption setting. The implementation complexity of the proposed encryption is considered, and it implies a suitable trade-off between increased security and increased implementation complexity

Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound

We introduce synchronization strings as a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than commonly considered half-errors, i.e., symbol corruptions and erasures. For every $\epsilon >0$, synchronization strings allow to index a sequence with an $\epsilon^{-O(1)}$ size alphabet such that one can efficiently transform $k$ synchronization errors into $(1+\epsilon)k$ half-errors. This powerful new technique has many applications. In this paper, we focus on designing insdel codes, i.e., error correcting block codes (ECCs) for insertion deletion channels. While ECCs for both half-errors and synchronization errors have been intensely studied, the later has largely resisted progress. Indeed, it took until 1999 for the first insdel codes with constant rate, constant distance, and constant alphabet size to be constructed by Schulman and Zuckerman. Insdel codes for asymptotically large or small noise rates were given in 2016 by Guruswami et al. but these codes are still polynomially far from the optimal rate-distance tradeoff. This makes the understanding of insdel codes up to this work equivalent to what was known for regular ECCs after Forney introduced concatenated codes in his doctoral thesis 50 years ago. A direct application of our synchronization strings based indexing method gives a simple black-box construction which transforms any ECC into an equally efficient insdel code with a slightly larger alphabet size. This instantly transfers much of the highly developed understanding for regular ECCs over large constant alphabets into the realm of insdel codes. Most notably, we obtain efficient insdel codes which get arbitrarily close to the optimal rate-distance tradeoff given by the Singleton bound for the complete noise spectrum

A Tutorial on Coding Methods for DNA-based Molecular Communications and Storage

Exponential increase of data has motivated advances of data storage technologies. As a promising storage media, DeoxyriboNucleic Acid (DNA) storage provides a much higher data density and superior durability, compared with state-of-the-art media. In this paper, we provide a tutorial on DNA storage and its role in molecular communications. Firstly, we introduce fundamentals of DNA-based molecular communications and storage (MCS), discussing the basic process of performing DNA storage in MCS. Furthermore, we provide tutorials on how conventional coding schemes that are used in wireless communications can be applied to DNA-based MCS, along with numerical results. Finally, promising research directions on DNA-based data storage in molecular communications are introduced and discussed in this paper

Codes for Synchronization in Channels and Sources with Edits

Edit channels are a class of communication channels where the output of the channel is an edited version of the input. The edits are considered to be deletions and insertions. DNA-based data storage system is one of the motivations for this model. This thesis studies various problems related to edit channel and also edit synchronization problem. Varshamov-Tenengolts (VT) codes are first introduced. These codes can correct a single deletion or insertion and have a linear-time decoder. The problem of efficient encoding of the non-binary version of VT codes is addressed, where a simple linear-time encoding method to systematically map binary message sequences onto VT codewords is proposed. Another model that is studied is segmented edit channels, where we have the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. A code construction is proposed for this model based on subsets of VT codes chosen with pre-determined prefxes and/or sufxes. Also an upper bound is derived 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. Edit synchronization is another problem studied in this thesis. In this model, there are two remote nodes (encoder and decoder), each having a binary sequence. The sequence X, available at the encoder, is the updated sequence and differs from Y (available at the decoder) by a small number of edits. The goal is to construct a message M, to be sent via a one-way error-free link, such that the decoder can reconstruct X using M and Y. A coding scheme is devised for this one-way synchronization model. The scheme is based on multiple layers of VT codes combined with off-the-shelf linear error-correcting codes and uses a list decoder. Motivated by the sequence reconstruction problem from traces in DNA-based storage, the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder is considered. A simple binary and non-binary code is proposed that splits the codeword into blocks and employs a VT code in each block. The availability of multiple traces helps the decoder to identify deletion-free copies of a block, and to avoid mis-synchronization while decoding. The encoding complexity of the proposed scheme is linear in the codeword length; the decoding complexity is linear in the codeword length and quadratic in the number of deletions and the number of traces. The list decoding technique for the proposed code is also considered

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many, short DNA strands. Second, the strands are stored in an unordered fashion inside the storage medium and each strand is replicated many times. Third, the data is accessed in an uncontrollable manner, i.e., random strands are drawn from the medium and received, possibly with errors. As one of our results, we show that there is a significant gap between the channel capacity and the achievable rate of a standard concatenated code in which one strand corresponds to an inner block. This is in fact surprising as for other channels, such as $q$-ary symmetric channels, concatenated codes are known to achieve the capacity. We further propose a modified concatenated coding scheme by combining several strands into one inner block, which allows to narrow the gap and achieve rates that are close to the capacity.Comment: Extended version of a paper submitted to International Symposium on Information Theory and Its Applications (ISITA) 202

Contemporary Coding Theory

Coding Theory naturally lies at the intersection of a large number of disciplines in pure and applied mathematics. A multitude of methods and means has been designed to construct, analyze, and decode the resulting codes for communication. This has suggested to bring together researchers in a variety of disciplines within Mathematics, Computer Science, and Electrical Engineering, in order to cross-fertilize generation of new ideas and force global advancement of the field. Areas to be covered are Network Coding, Subspace Designs, General Algebraic Coding Theory, Distributed Storage and Private Information Retrieval (PIR), as well as Code-Based Cryptography

The information capacity of the genetic code: Is the natural code optimal?

We envision the molecular evolution process as an information transfer process and provide a quantitative measure for information preservation in terms of the channel capacity according to the channel coding theorem of Shannon. We calculate Information capacities of DNA on the nucleotide (for non-coding DNA) and the amino acid (for coding DNA) level using various substitution models. We extend our results on coding DNA to a discussion about the optimality of the natural codon-amino acid code. We provide the results of an adaptive search algorithm in the code domain and demonstrate the existence of a large number of genetic codes with higher information capacity. Our results support the hypothesis of an ancient extension from a 2-nucleotide codon to the current 3-nucleotide codon code to encode the various amino acids