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We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations at intermediate nodes consist of only circular-shifts and bitwise addition (XOR). Departing from existing literature, we systematically formulate circular-shift LNC as a special type of vector LNC, where the local encoding kernels of an L-dimensional circular-shift linear code of degree δ...
Lattice network coding is an important building block of physical-layer network coding. The receiver is required to compute a linear combination of the source symbols belonging to a finite alphabet with an algebraic structure. In this paper, lattice network codes are constructed from lattices that have optimal packing density and the best known shaping gain in low dimensions. Using the efficient quantization...
A combinatorial notion of flow is identified for timeinvariant linear coding over non-layered deterministic linear networks that may contain cycles, broadcast and interference links. It reveals the matroidal structure for efficient code construction, and enables a seamless extension of the classical network coding results. In particular, the flow can be decomposed efficiently into disjoint information...
In this paper, we propose a novel opportunistic pair-wise transmission scheme in a multi-way relay channel (MWRC), in which multiple users exchange information via a common relay. We investigate pair-wise compute-and-forward for MWRCs by exploiting the multi-user fading channels. Conventionally, a pair-wise physical-layer network coding scheme with binary phase shift keying modulation was studied...
In this paper, we investigate lattice network codes (LNCs) constructed from lattices over the ring of Eisenstein integers. Quantization and encoding algorithms over Eisenstein integers are first introduced. Then, a union bound estimation (UBE) of the decoding error probability is derived when the shaping region of the LNC is a product of regular hexagons. We show that the UBE is in the same form as...
On an acyclic network, generic linear network codes are known to have the strongest optimality in terms of linear independence. This paper characterizes other properties of generic codes on a given acyclic network. We first show that every generic code is variable-rate generic with the additional property that the coding coefficients in relation to data-generating edges need not be changed. We next...
In this work, we define delay invariant convolutional network codes which guarantee multicast communication at asymptotically optimal rates in networks with arbitrary delay patterns. We show the existence of such a code over every symbol field. Moreover, the code can be constructed with high probability when coding coefficients are independently and uniformly chosen from a sufficiently large set of...
Unequal error/erasure protection (UEP) is often employed in multilayer video streaming to ensure successful reception of the important reference layers. In this paper, we investigate possible ways to provide such protection to the multicasting sessions of scalable video codes (SVC) using randomized linear network codes (RLNCs). We surmised that it takes both proper combination of transmitted symbols...
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