Related papers: On Function-Correcting Codes
In this paper, we provide a performance analysis of a new class of serial concatenated convolutional codes (SCCC) where the inner encoder can be punctured beyond the unitary rate. The puncturing of the inner encoder is not limited to inner…
Code-trained language models have proven to be highly effective for various code intelligence tasks. However, they can be challenging to train and deploy for many software engineering applications due to computational bottlenecks and memory…
In this paper, we use entropy functions to characterise the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems. We show that when sources are colocated,…
Recently a powerful class of rate-compatible serially concatenated convolutional codes (SCCCs) have been proposed based on minimizing analytical upper bounds on the error probability in the error floor region. Here this class of codes is…
In this paper, we consider different aspects of the network functional compression problem where computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of…
Many programmers, when they encounter an error, would like to have the benefit of automatic fix suggestions---as long as they are, most of the time, adequate. Initial research in this direction has generally limited itself to specific…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
The rapidly improving performance of modern hardware renders convolutional codes obsolete, and allows for the practical implementation of more sophisticated correction codes such as low density parity check (LDPC) and turbo codes (TC). Both…
In general, approximating classes of functions defined over high-dimensional input spaces by linear combinations of a fixed set of basis functions or ``features'' is known to be hard. Typically, the worst-case error of the best basis set…
A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate, its value at a codeword…
We study the reliability function of general classical-quantum channels, which describes the optimal exponent of the decay of decoding error when the communication rate is below the capacity. As the main result, we prove a lower bound, in…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…
Functional dependence graph (FDG) is an important class of directed graph that captures the dominance relationship among a set of variables. FDG is frequently used in calculating network coding capacity bounds. However, the order of FDG is…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
Given a connected finite graph $G$, an integer-valued function $f$ on $V(G)$ is called $M$-Lipschitz if the value of $f$ changes by at most $M$ along the edges of $G$. In 2013, Peled, Samotij, and Yehudayoff showed that random $M$-Lipschitz…
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem as well as nonuniform demands such…
Already in the 1960s, Levenshtein and others studied error-correcting codes that protect against synchronization errors, such as symbol insertions and deletions. However, despite significant efforts, progress on designing such codes has…
Defect-adaptive surface-code methods have substantially advanced the construction of valid logical patches on imperfect hardware, but fault-tolerant computation also requires executable logical oper ations on the resulting irregular…