Related papers: Robust Gray Codes Approaching the Optimal Rate
We introduce the \emph{graphical reconfigurable circuits (GRC)} model as an abstraction for distributed graph algorithms whose communication scheme is based on local mechanisms that collectively construct long-range reconfigurable channels…
For any black-box model, conformal prediction (CP) returns prediction sets guaranteed to include the true label with high adjustable probability. Robust CP (RCP) extends the guarantee to the worst case noise up to a pre-defined magnitude.…
We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The…
We show a nearly optimal lower bound on the length of linear relaxed locally decodable codes (RLDCs). Specifically, we prove that any $q$-query linear RLDC $C\colon \{0,1\}^k \to \{0,1\}^n$ must satisfy $n = k^{1+\Omega(1/q)}$. This bound…
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
This paper addresses the design of a dedicated homophonic coding for a class of communication systems which, in order to provide both reliability and security, first encode the data before encrypting it, which is referred to as the…
We continue the investigation of locally testable codes, i.e., error-correcting codes for whom membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on…
This paper introduces a novel approach called "friendly attack" aimed at enhancing the performance of error correction channel codes. Inspired by the concept of adversarial attacks, our method leverages the idea of introducing slight…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
Precoded polar product codes are proposed, where selected component codes enable successive cancellation list decoding to generate bit-wise soft messages efficiently for iterative decoding while targeting optimized distance spectrum as…
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…
We establish that it is possible to extract accurate blockwise and bitwise soft output from Guessing Codeword Decoding with minimal additional computational complexity by considering it as a variant of Guessing Random Additive Noise…
Interactive coding allows two parties to conduct a distributed computation despite noise corrupting a certain fraction of their communication. Dani et al.\@ (Inf.\@ and Comp., 2018) suggested a novel setting in which the amount of noise is…
The robust coding of natural images and the effective compression of encrypted images have been studied individually in recent years. However, little work has been done in the robust coding of encrypted images. The existing results in these…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Guessing Random Additive Noise Decoding (GRAND) is a family of universal decoding algorithms suitable for decoding any moderate redundancy code of any length. We establish that, through the use of list decoding, soft-input variants of GRAND…
To improve the off-sample generalization of classical procedures minimizing the empirical risk under potentially heavy-tailed data, new robust learning algorithms have been proposed in recent years, with generalized median-of-means…