اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNetwork Coding for $3$s$/n$t Sum-Networks
160
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A sum-network is a directed acyclic network where each source independently generates one symbol from a given field $mathbb F$ and each terminal wants to receive the sum $($over $mathbb F)$ of the source symbols. For sum-networks with two sources or two terminals, the solvability is characterized by the connection condition of each source-terminal pair [3]. A necessary and sufficient condition for the solvability of the $3$-source $3$-terminal $(3$s$/3$t$)$ sum-networks was given by Shenvi and Dey [6]. However, the general case of arbitrary sources/sinks is still open. In this paper, we investigate the sum-network with three sources and $n$ sinks using a region decomposition method. A sufficient and necessary condition is established for a class of $3$s$/n$t sum-networks. As a direct application of this result, a necessary and sufficient condition of solvability is obtained for the special case of $3$s$/3$t sum-networks.
قيم البحث
اقرأ أيضاً
Modern medical wireless systems, such as wireless body area networks (WBANs), are applications of wireless networks that can be used as a tool of data transmission between patients and doctors. Accuracy of data transmission is an important requiremen
t for such systems. In this paper, we will propose a WBAN which is robust against erasures and describe its properties using graph theoretic techniques.
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 ar
e 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.
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 ar
e 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.
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 bu
t 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.
Universal quantum computation requires the implementation of a logical non-Clifford gate. In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical $T$ and $T^{-1}$ gates. For example, this could enable mag
ic state distillation with non-CSS codes and, thus, provide better parameters than CSS-based protocols. However, among non-degenerate stabilizer codes that support transversal $T$, we prove that CSS codes are optimal. We also show that triorthogonal codes are, essentially, the only family of CSS codes that realize logical transversal $T$ via physical transversal $T$. Using our algebraic approach, we reveal new purely-classical coding problems that are intimately related to the realization of logical operations via transversal $T$. Decreasing monomial codes are also used to construct a code that realizes logical CCZ. Finally, we use Axs theorem to characterize the logical operation realized on a family of quantum Reed-Muller codes. This result is generalized to finer angle $Z$-rotations in arXiv:1910.09333.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
