Related papers: Block Edit Errors with Transpositions: Determinist…
In this paper, we investigate the problem of designing $(n, N; \mathcal{B})$-reconstruction codes for $N\in \{14,11,9,5\}$, where $\mathcal{B}$ is the single-deletion single-substitution ball function that maps a sequence to the set of all…
We consider interactive coding in a setting where $n$ parties wish to compute a joint function of their inputs via an interactive protocol over imperfect channels. We assume that adversarial errors can comprise a $\mathcal{O}(\frac{1}{n})$…
We develop deterministic algorithms for the problems of consensus, gossiping and checkpointing with nodes prone to failing. Distributed systems are modeled as synchronous complete networks. Failures are represented either as crashes or…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem ($\mathsf{GHD}^n_{L, U}$): Alice and Bob are given binary string of length $n$ and they are guaranteed that Hamming distance between their…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
Various vulnerabilities have been found in message parsers of protocol implementations in the past. Even highly sensitive software components like TLS libraries are affected regularly. Resulting issues range from denial-of-service attacks…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
Determinant codes are a class of exact-repair regenerating codes for distributed storage systems with parameters (n, k = d, d). These codes cover the entire trade-off between per-node storage and repair-bandwidth. In an earlier work of the…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Motivated by DNA storage systems and 3D fingerprinting, this work studies the adversarial torn paper channel with edit errors. This channel first applies at most $t_e$ edit errors (i.e., insertions, deletions, and substitutions) to the…
Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…
In interactive coding, Alice and Bob wish to compute some function $f$ of their individual private inputs $x$ and $y$. They do this by engaging in an interactive protocol to jointly compute $f(x,y)$. The goal is to do this in an…
This paper considers multiplexing two sequences of messages with two different decoding delays over a packet erasure channel. In each time slot, the source constructs a packet based on the current and previous messages and transmits the…
We consider the problem of data exchange by a group of closely-located wireless nodes. In this problem each node holds a set of packets and needs to obtain all the packets held by other nodes. Each of the nodes can broadcast the packets in…
We consider error correction in quantum key distribution. To avoid that Alice and Bob unwittingly end up with different keys precautions must be taken. Before running the error correction protocol, Bob and Alice normally sacrifice some bits…
Simultaneous dense coding guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to "lock" the…
This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes.…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
This paper addresses the problem of constructing MDS codes that enable exact repair of each code block with small repair bandwidth, which refers to the total amount of information flow from the remaining code blocks during the repair…