Related papers: Network Coding Based on Byte-wise Circular Shift a…
In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity order or the transmission rate…
Addition is perhaps one of the simplest arithmetic tasks one can think of and is usually performed using the carrying over algorithm. This algorithm consists of two tasks: adding digits in the same position and carrying over a one whenever…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
Repeated root Cyclic and Negacyclic codes over Galois rings have been studied much less than their simple root counterparts. This situation is beginning to change. For example, repeated root codes of length $p^s$, where $p$ is the…
The technique for hardware multiplication based upon Fourier transformation has been introduced. The technique has the highest efficiency on multiplication units with up to 8 bit range. Each multiplication unit is realized on base of the…
A new communication scheme for Gaussian parallel relay networks based on superposition coding and partial decoding at the relays is presented. Some specific examples are proposed in which two codebook layers are superimposed. The first…
Existing construction algorithms of block network-error correcting codes require a rather large field size, which grows with the size of the network and the number of sinks, and thereby can be prohibitive in large networks. In this work, we…
A general and fast method is conceived for computing the cyclic convolution of n points, where n is a prime number. This method fully exploits the internal structure of the cyclic matrix, and hence leads to significant reduction of the…
Random linear network coding (RLNC) in theory achieves the max-flow capacity of multicast networks, at the cost of high decoding complexity. To improve the performance-complexity tradeoff, we consider the design of sparse network codes. A…
We construct trace codes over $\Z_4$ by using Boolean functions and skew sets, respectively. Their Lee weight distribution is studied by using a Galois ring version of the Walsh-Hadamard transform and exponential sums. We obtain a new…
In this paper, we investigate transmission techniques for a fundamental cooperative cognitive radio network, i.e., a radio system where a Secondary user may act as relay for messages sent by the Primary user, hence offering performance…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
Boolean cardinality constraints state that at most (at least, or exactly) $k$ out of $n$ propositional literals can be true. We propose a new class of selection networks that can be used for an efficient encoding of them. Several comparator…
In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give applications to the characterization of the splitting primes…
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…
Galois field (GF) arithmetic is used to implement critical arithmetic components in communication and security-related hardware, and verification of such components is of prime importance. Current techniques for formally verifying such…
The applications in the critical infrastructure systems pose simultaneous resilience and performance requirements to the underlying computer network. To meet such requirements, the networks that use the store-and-forward paradigm poses…
Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic…
A message-passing algorithm for counting short cycles in a graph is presented. For bipartite graphs, which are of particular interest in coding, the algorithm is capable of counting cycles of length g, g +2,..., 2g - 2, where g is the girth…