Related papers: Message Encoding for Spread and Orbit Codes
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system.…
An unconventional encoding scheme called concurrent coding, has recently been demonstrated and shown to offer interesting features and benefits in comparison to conventional techniques, e.g. robustness against burst errors and improved…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
We consider the problem of slotted asynchronous coded communication, where in each time frame (slot), the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide…
For the information transmission over a binary symmetric channel the random coding is used. The transmission of exponential number of messages is considered. The exact decoding error probability exponent is derived. The proof is based on…
Network coding is a highly efficient data dissemination mechanism for wireless networks. Since network coded information can only be recovered after delivering a sufficient number of coded packets, the resulting decoding delay can become…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a…
Error and erasure exponents for the broadcast channel with degraded message sets are analyzed. The focus of our error probability analysis is on the main receiver where, nominally, both messages are to be decoded. A two-step decoding…
In order to communicate a message over a noisy channel, a sender (Alice) uses an error-correcting code to encode her message $x$ into a codeword. The receiver (Bob) decodes it correctly whenever there is at most a small constant fraction of…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
Subspace codes have recently been used for error correction in random network coding. In this work, we focus on one-orbit cyclic subspace codes. If $S$ is an $\mathbb{F}_q$-subspace of $\mathbb{F}_{q^n}$, then the one-orbit cyclic subspace…
We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform…
Distributed storage systems often introduce redundancy to increase reliability. When coding is used, the repair problem arises: if a node storing encoded information fails, in order to maintain the same level of reliability we need to…
An index code for a broadcast channel with receiver side information is 'locally decodable' if every receiver can decode its demand using only a subset of the codeword symbols transmitted by the sender instead of observing the entire…
This paper studies a special class of multicast index coding problems where a sender transmits messages to multiple receivers, each with some side information. Here, each receiver knows a unique message a priori, and there is no restriction…
We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality…
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…
This paper investigates the decoding of certain Gabidulin codes that were transmitted over a channel with space-symmetric errors. Space-symmetric errors are additive error matrices that have the property that their column and row spaces are…