Trustworthy Communications across Parallel Asynchronous Channels with Glitches

Transmission across asynchronous communication channels is subject to laser injection attacks which cause glitches – pulses that are added to the transmitted signal at arbitrary times. This paper presents self-synchronizing zero-latency or near zero-latency coding schemes that require no acknowledge and can perfectly decode any transmission distorted by glitches (as long as the percentage of glitches is not too large)

File Updates Under Random/Arbitrary Insertions And Deletions

A client/encoder edits a file, as modeled by an insertion-deletion (InDel) process. An old copy of the file is stored remotely at a data-centre/decoder, and is also available to the client. We consider the problem of throughput- and computationally-efficient communication from the client to the data-centre, to enable the server to update its copy to the newly edited file. We study two models for the source files/edit patterns: the random pre-edit sequence left-to-right random InDel (RPES-LtRRID) process, and the arbitrary pre-edit sequence arbitrary InDel (APES-AID) process. In both models, we consider the regime in which the number of insertions/deletions is a small (but constant) fraction of the original file. For both models we prove information-theoretic lower bounds on the best possible compression rates that enable file updates. Conversely, our compression algorithms use dynamic programming (DP) and entropy coding, and achieve rates that are approximately optimal.Comment: The paper is an extended version of our paper to be appeared at ITW 201

An Upper Bound on the Capacity of non-Binary Deletion Channels

We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability $d$, denoted by $C_{2K}(d)$, and the capacity of the binary deletion channel with the same deletion probability, $C_2(d)$, that is, $C_{2K}(d)\leq C_2(d)+(1-d)\log(K)$. Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as $d \rightarrow 0$.Comment: accepted for presentation in ISIT 201

Coding over Sets for DNA Storage

In this paper, we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where data is represented by an unordered set of $M$ sequences, each of length $L$. Errors within that model are losses of whole sequences and point errors inside the sequences, such as substitutions, insertions and deletions. We propose code constructions which can correct these errors with efficient encoders and decoders. By deriving upper bounds on the cardinalities of these codes using sphere packing arguments, we show that many of our codes are close to optimal.Comment: 5 page

A Note on the Deletion Channel Capacity

Memoryless channels with deletion errors as defined by a stochastic channel matrix allowing for bit drop outs are considered in which transmitted bits are either independently deleted with probability $d$ or unchanged with probability $1-d$. Such channels are information stable, hence their Shannon capacity exists. However, computation of the channel capacity is formidable, and only some upper and lower bounds on the capacity exist. In this paper, we first show a simple result that the parallel concatenation of two different independent deletion channels with deletion probabilities $d_1$ and $d_2$, in which every input bit is either transmitted over the first channel with probability of $\lambda$ or over the second one with probability of $1-\lambda$, is nothing but another deletion channel with deletion probability of $d=\lambda d_1+(1-\lambda)d_2$. We then provide an upper bound on the concatenated deletion channel capacity $C(d)$ in terms of the weighted average of $C(d_1)$, $C(d_2)$ and the parameters of the three channels. An interesting consequence of this bound is that $C(\lambda d_1+(1-\lambda))\leq \lambda C(d_1)$ which enables us to provide an improved upper bound on the capacity of the i.i.d. deletion channels, i.e., $C(d)\leq 0.4143(1-d)$ for $d\geq 0.65$. This generalizes the asymptotic result by Dalai as it remains valid for all $d\geq 0.65$. Using the same approach we are also able to improve upon existing upper bounds on the capacity of the deletion/substitution channel.Comment: Submitted to the IEEE Transactions on Information Theor