Related papers: Coding Theorems for a (2,2)-Threshold Scheme with …
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…
We study the arithmetic circuit complexity of threshold secret sharing schemes by characterizing the graph-theoretic properties of arithmetic circuits that compute the shares. Using information inequalities, we prove that any unrestricted…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
We consider the two scenarios of communicating a pair $S_{1},S_{2}$ of correlated sources over multiple access (MAC) and interference channels (IC) respectively. We undertake a Shannon theoretic study and focus on achievability, i.e.,…
This paper investigates the secret key authentication capacity region. Specifically, the focus is on a model where a source must transmit information over an adversary controlled channel where the adversary, prior to the source's…
For a given family of spatially coupled codes, we prove that the LP threshold on the BSC of the graph cover ensemble is the same as the LP threshold on the BSC of the derived spatially coupled ensemble. This result is in contrast with the…
We consider the problem of encoding range minimum queries (RMQs): given an array A[1..n] of distinct totally ordered values, to pre-process A and create a data structure that can answer the query RMQ(i,j), which returns the index containing…
Coding theory plays a crucial role in ensuring data integrity and reliability across various domains, from communication to computation and storage systems. However, its reliance on trust assumptions for data recovery, which requires the…
We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition. Lower bounds are obtained by considering…
We study the convergence rates of the EM algorithm for learning two-component mixed linear regression under all regimes of signal-to-noise ratio (SNR). We resolve a long-standing question that many recent results have attempted to tackle:…
This paper investigates a joint source-channel secrecy problem for the Shannon cipher broadcast system. We suppose list secrecy is applied, i.e., a wiretapper is allowed to produce a list of reconstruction sequences and the secrecy is…
We introduce a new measure on secrecy, which is established based on rate-distortion theory. It is named \emph{security rate}, which is the minimum (infimum) of the additional rate needed to reconstruct the source within target distortion…
The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit…
A (t,n)-threshold secret sharing scheme is a method to distribute a secret among n participants in such a way that any t participants can recover the secret, but no t-1 participants can. In this paper, we propose two secret sharing schemes…
Code Large Language Models (LLMs) have demonstrated remarkable capabilities in generating, understanding, and manipulating programming code. However, their training process inadvertently leads to the memorization of sensitive information,…
Coding theory revolves around the incorporation of redundancy into transmitted symbols, computation tasks, and stored data to guard against adversarial manipulation. However, error correction in coding theory is contingent upon a strict…
We consider a secure source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source X and wishes to transmit this source losslessly to Bob over a rate-limited link.…
Advances in reverse engineering make it challenging to deploy any on-chip information in a way that is hidden from a determined attacker. A variety of techniques have been proposed for design obfuscation including look-alike cells in which…
In this paper, new inner and outer bounds on the achievable compression-equivocation rate region for generalized secure data compression with side information are given that do not match in general. In this setup, two senders, Alice and…