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Signal-time coding, which combines the traditional encoding/modulation mode in the signal domain with signal pulse phase modulation in the time domain, was proposed to improve the information flow rate in relay networks. In this paper, we…
In this paper, we study the performance of network-coded cooperative diversity systems with practical communication constraints. More specifically, we investigate the interplay between diversity, coding, and multiplexing gain when the relay…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising…
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a class of three-weight…
We consider a communication scenario where a source communicates with a destination over a directed layered relay network. Each relay performs analog network coding where it scales and forwards the signals received at its input. In this…
The theory of colorful graphs can be developed by working in Galois field modulo (p), p > 2 and a prime number. The paper proposes a program of possible conversion of graph theory into a pleasant colorful appearance. We propose to paint the…
We give an algorithm for finding network encoding and decoding equations for error-free multicasting networks with multiple sources and sinks. The algorithm given is efficient (polynomial complexity) and works on any kind of network…
A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo $2^{m}$ is a linear code with property that if the codeword $(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift $(c_1,c_2,...,c_0)\in \mathcal{C}$.…
In this paper, we describe linear and cyclic codes over the rings of the form $R_{s,p}=\mathbb{Z}_{p}[u]/\left( f\left(u\right) /\left( u-s\right) \right)$, where $p$ is a prime number and $f\left( u\right) =u^{p}-u$, with $s\in…
This paper presents a novel algorithm for the modulus operation for FPGA implementation. The proposed algorithm use only addition, subtraction, logical, and bit shift operations, avoiding the complexities and hardware costs associated with…
Likelihood-based generative models are the backbones of lossless compression due to the guaranteed existence of codes with lengths close to negative log likelihood. However, there is no guaranteed existence of computationally efficient…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
This paper shows how network coding and superdense coding can be combined to increase the classical data throughput by a factor $2-\epsilon$ (for arbitrarily small $\epsilon > 0$) compared to the maximum that could be achieved using either…
Predictive coding (PC) networks are a biologically interesting class of neural networks. Their layered hierarchy mimics the reciprocal connectivity pattern observed in the mammalian cortex, and they can be trained using local learning rules…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which…
Network coding has proved its efficiency in increasing the network performance for traditional ad-hoc networks. In this paper, we investigate using network coding for enhancing the throughput of multi-hop cognitive radio networks. We…
Any permutation polynomial is an $ n $-cycle permutation. When $n$ is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These…