Related papers: Message Encoding for Spread and Orbit Codes
Spread codes and cyclic orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability, transmission rate and decoding methods, but the question of how to…
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
In network coding a constant dimension code consists of a set of k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
In the setting of error correcting codes, Alice wants to send a message $x \in \{0,1\}^n$ to Bob via an encoding $\text{enc}(x)$ that is resilient to error. In this work, we investigate the scenario where Bob is a low space decoder. More…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
In the literature there exists analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this work, we look into the probability that the…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
Motivated by signal processing, we present a new class of channel codes, called signal codes, for continuous-alphabet channels. Signal codes are lattice codes whose encoding is done by convolving an integer information sequence with a fixed…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Pl\"ucker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words.
Secure communication protocols are often formulated in a paradigm where the message is encoded in measurement outcomes. In this work we propose a rather unexplored framework in which the message is encoded in measurement settings rather…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
This paper considers the problem of simultaneously communicating two messages, a high-security message and a low-security message, to a legitimate receiver, referred to as the security embedding problem. An information-theoretic formulation…
Orbit codes are a family of codes employable for communications on a random linear network coding channel. The paper focuses on the classification of these codes. We start by classifying the conjugacy classes of cyclic subgroups of the…
We study the theoretical performance of a combined approach to demodulation and decoding of binary continuous-phase modulated signals under repetition-like codes. This technique is motivated by a need to transmit packetized or framed data…
We derive universal codes for transmission of broadcast and confidential messages over classical-quantum-quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct…