Citation Context

...near combinations. Owing to space limitations, we do not attempt a full survey of the literature. We refer interested readers to [2] for additional references pertaining to compute-and-forward and to =-=[6]-=-, [7] for surveys of the closely related topic of physical-layer network coding. II. PROBLEM STATEMENT Our setting is nearly identical to that of [2] and we reproduce some of the key definitions below...

Citation Context

...o-way relay networks, a nested lattice based strategy has been developed that the achievable rate is near the optimal upper bound [21]-[23]. Recently, a new strategy of compute-and-forward (CPF) [24]-=-=[25]-=-, beneficial from both network coding and lattice codes, attracts great attention. The main idea is that a relay will decode a linear function of transmitted messages according to the observed channel...

Citation Context

...-layer network coding, Soft demodulation, Realtime 1. INTRODUCTION Since the introduction of the concept of PNC [1,2] in 2006, it has developed into a subfield of network coding with a wide following =-=[3,4]-=-. Figure 1 illustrates the concept of PNC when it is applied to a two-way relay channel (TWRC). In TWRC, two end nodes A and B exchange information via a relay R. The information exchange consists of ...

Citation Context

... in physical layer with such lattices has been realized to asymptotically approach the capacity for the bidirectional relay networks in [21] [22] [23] [24]. The reader is referred to a tutorial paper =-=[25]-=- for more details about using lattices for the bidirectional relay channels. One of the main contribution of [1] is to provide a means to harness interference when there is no channel state informatio...

Citation Context

...ear combination of messages. Once enough linear combinations are obtained the original messages can be retrieved. The concept of physical-layer network coding is studied in, for instance [1]–[7]. See =-=[8]-=- for a survey of recent results. In [1]–[3] the aim is to obtain linear combinations reliably. In contrast, in [4]–[7] one is satisfied with a noisy version of these linear combinations. In [9] the ap...

Citation Context

...of schemes, dubbed physical-layer network coding, has been proposed to harness the interference property of the wireless medium, through the use of codebooks with appropriate algebraic structure (see =-=[9]-=- for a recent survey). For instance, compute-and-forward enables relays to recover equations of the transmitted messages and pass them towards the destinations [10]. Until recently, these two broad st...

Citation Context

...t to 2000 (33 dB), in the case of L = 2 sources. The results are sorted and provided in Tabel 1. As an example, in Fig. 3, the distance between point F and the origin is equal to ‖gmin (ek)‖ for ek = =-=[2, 1]-=- T . Now, according to the Lemma 4, for a given gm, equivalent to a constant instantaneous sum SNR, only ECVs that satisfy ‖gmin (am)‖ ≤ ‖gm‖ are needed to be searched. These ECVs can be found from Ta...

Citation Context

...des attempt to decode the modulo-two sum (XOR) of the transmitted messages. Several network coding realizations in wireless networks are discussed in [7]-[11]. Compute-and-forward (CPF) strategy [12]-=-=[13]-=- is a promising new approach to physical-layer network coding for general wireless networks, beneficial from both network coding and lattice codes [14]-[15]. The main idea is that a relay will decode ...

Citation Context

...been developed for systems with multiantenna nodes [12] and asynchronous scenarios [13]–[15]. For a more extensive coverage of the twoway relay network with PNC, see the tutorial by Nazer and Gastpar =-=[16]-=- as well as Liew et al. [17]. The denoising scheme for the two-way relay network depends on the modulation adopted for transmission in the MA phase. When the two users transmit binary phase-shift keyi...