Related papers: Unbounded Error Correcting Codes
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied.…
We study two basic problems regarding edit error, i.e. document exchange and error correcting codes for edit errors (insdel codes). For message length $n$ and edit error upper bound $k$, it is known that in both problems the optimal sketch…
The maximum operational range of continuous variable quantum key distribution protocols has shown to be improved by employing high-efficiency forward error correction codes. Typically, the secret key rate model for such protocols is…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
We consider the \emph{functional index coding problem} over an error-free broadcast network in which a source generates a set of messages and there are multiple receivers, each holding a set of functions of source messages in its cache,…
Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for…
Recovery of data packets from packet erasures in a timely manner is critical for many streaming applications. An early paper by Martinian and Sundberg introduced a framework for streaming codes and designed rate-optimal codes that permit…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same…
We consider analog error-correcting codes (analog ECCs) that are designed to correct/detect outlying errors arising in analog implementations of vector-matrix multiplication. The error-correction/detection capability of an analog ECC can be…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
Emerging applications in manufacturing, wireless communication, and molecular data storage require robust coding schemes that remain effective under physical distortions where codewords may be arbitrarily fragmented and partially missing.…
We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state…
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…
Coded caching is used to reduce network congestion during peak hours. A single server is connected to a set of users through a bottleneck link, which generally is assumed to be error-free. During non-peak hours, all the users have full…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…