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Added by
Litian Liu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In this paper we introduce Neural Network Coding(NNC), a data-driven approach to joint source and network coding. In NNC, the encoders at each source and intermediate node, as well as the decoder at each destination node, are neural networks which are all trained jointly for the task of communicating correlated sources through a network of noisy point-to-point links. The NNC scheme is application-specific and makes use of a training set of data, instead of making assumptions on the source statistics. In addition, it can adapt to any arbitrary network topology and power constraint. We show empirically that, for the task of transmitting MNIST images over a network, the NNC scheme shows improvement over baseline schemes, especially in the low-SNR regime.
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Slotted ALOHA can benefit from physical-layer network coding (PNC) by decoding one or multiple linear combinations of the packets simultaneously transmitted in a timeslot, forming a system of linear equations. Different systems of linear equations are recovered in different timeslots. A message decoder then recovers the original packets of all the users by jointly solving multiple systems of linear equations obtained over different timeslots. We propose the batched BP decoding algorithm that combines belief propagation (BP) and local Gaussian elimination. Compared with pure Gaussian elimination decoding, our algorithm reduces the decoding complexity from cubic to linear function of the number of users. Compared with the ordinary BP decoding algorithm for low-density generator-matrix codes, our algorithm has better performance and the same order of computational complexity. We analyze the performance of the batched BP decoding algorithm by generalizing the tree-based approach and provide an approach to optimize the system performance.
Leveraging recent progress in physical-layer network coding we propose a new approach to random access: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission, the receiver can thus obtain many linear combinations and eventually recover all original packets. This is by contrast to slotted ALOHA where packet collisions lead to complete erasures. The throughput of the proposed strategy is derived and shown to be significantly superior to the best known strategies, including multipacket reception.
For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class $mathcal{N}$ of multicast networks and obtain an explicit formula for the linear solvability of these networks, which involves the associated coset numbers of a multiplicative subgroup in a base field. The concise formula turns out to be the first that matches the topological structure of a multicast network and algebraic identities of a field other than size. It further facilitates us to unveil emph{infinitely many} new multicast networks linearly solvable over GF($q$) but not over GF($q$) with $q < q$, based on a subgroup order criterion. In particular, i) for every $kgeq 2$, an instance in $mathcal{N}$ can be found linearly solvable over GF($2^{2k}$) but emph{not} over GF($2^{2k+1}$), and ii) for arbitrary distinct primes $p$ and $p$, there are infinitely many $k$ and $k$ such that an instance in $mathcal{N}$ can be found linearly solvable over GF($p^k$) but emph{not} over GF($p^{k}$) with $p^k < p^{k}$. On the other hand, the construction of $mathcal{N}$ also leads to a new class of multicast networks with $Theta(q^2)$ nodes and $Theta(q^2)$ edges, where $q geq 5$ is the minimum field size for linear solvability of the network.
This paper investigates noncoherent detection in a two-way relay channel operated with physical layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, hence the performance of the noncoherent detector is independent of the phase. PNC, however, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector in PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we do away from preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols. Numerical results show that our detector performs nearly as well as a fictitious optimal detector that has perfect knowledge of the channel gains and relative phase.
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two well-known LNEC coding approaches. Furthermore, by developing a graph-theoretic approach to the framework of LNEC coding, we obtain a significantly enhanced characterization of the error correction capability of LNEC codes in terms of the minimum distances at the sink nodes. In LNEC coding, the minimum required field size for the existence of LNEC codes, in particular LNEC maximum distance separable (MDS) codes which are a type of most important optimal codes, is an open problem not only of theoretical interest but also of practical importance, because it is closely related to the implementation of the coding scheme in terms of computational complexity and storage requirement. By applying the graph-theoretic approach, we obtain an improved upper bound on the minimum required field size. The improvement over the existing results is in general significant. The improved upper bound, which is graph-theoretic, depends only on the network topology and requirement of the error correction capability but not on a specific code construction. However, this bound is not given in an explicit form. We thus develop an efficient algorithm that can compute the bound in linear time. In developing the upper bound and the efficient algorithm for computing this bound, various graph-theoretic concepts are introduced. These concepts appear to be of fundamental interest in graph theory and they may have further applications in graph theory and beyond.
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