Related papers: Network Coding Based on Byte-wise Circular Shift a…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
We present here some results of applying the Cayley-Dickson process to certain alternative algebras (notably built upon Galois fields and congruence rings), in a manner which might yield new building blocks for cryptographic systems. We…
We consider the special case of index coding over the Gaussian broadcast channel where each receiver has prior knowledge of a subset of messages at the transmitter and demands all the messages from the source. We propose a concatenated…
In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [3] that only certain combinations of the…
Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…
Most of the work on implementing arithmetic on a quantum computer has borrowed from results in classical reversible computing (e.g. [VBE95], [BBF02], [DKR04]). These quantum networks are inherently classical, as they can be implemented with…
In network coding, a flag code is a set of sequences of nested subspaces of $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Flag codes defined as orbits of a cyclic subgroup of the general linear group acting on…
Stars and cycles are basic structures in network construction. The former has been well studied in network analysis, while the latter attracted rare attention. A node together with its neighbors constitute a neighborhood star-structure…
Z2Z4-additive codes have been defined as a subgroup of Z2^{r} x Z4^{s} in [5] where Z2, Z4 are the rings of integers modulo 2 and 4 respectively and r and s positive integers. In this study, we define a new family of codes over the set…
We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The…
We present a simple method for the construction of polynomials with cyclic Galois groups, hoping to encourage a reader with some background in algebra to make computations of his/her own.
The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay…
A new incremental algorithm for data compression is presented. For a sequence of input symbols algorithm incrementally constructs a p-adic integer number as an output. Decoding process starts with less significant part of a p-adic integer…
Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by…
A new coding scheme for general N-node relay networks is presented for unicast, multicast, and broadcast. The proposed distributed decode-forward scheme combines and generalizes Marton coding for single-hop broadcast channels and the…
In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…
This paper concerns with the construction of codes over $GF(2)$ which reach the max-flow for single source multicast acyclic networks with delay. The coding is always a bitwise XOR of packets with equal lengths, and is based on highly…
Let $R=\mathbb{Z}_4$ be the integer ring mod $4$. A double cyclic code of length $(r,s)$ over $R$ is a set that can be partitioned into two parts that any cyclic shift of the coordinates of both parts leaves invariant the code. These codes…