sequential network

sequential network

[si′kwen·chəl ′net‚wərk]
(computer science)
An idealized model of a sequential circuit that reflects its logical but not its electronic properties.
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In this paper, we build upon our work in [15] motivated by reducing the number of the sequential network decoding steps using Combined Packet/symbol Network Coding (CPNC) per source per unit time providing the framework for data exchange for more than two receivers, with applying the PUMTC as the channel coding for FEC technique.
The rest of the paper is organized as in the following order: Section II explains why applying CPNC system tents to reduce the sequential network decoding steps used in MSNC [15].
Finally, for both [AF.sub.P] and [DF.sub.p], L - 1 separate packets [??] are broadcasted with the combined packet/symbol shown in Equations (3) and (5) to be used in the sequential network decoding steps for [AF.sub.p] and [DF.sub.P] respectively.
Figure 1 shows that in CPNC, the number of the sequential network decoding steps has been decreased by L - 1 per user, which is N (L - 1) in total, as these packets are being broadcasted directly as Amplify-and-Forward Benchmark ([AF.sub.b]) or Decode-and-forward Benchmark ([DF.sub.b]) that need no any sequential network decoding steps to retrieve.
Figure 2 illustrates the serial sequential network decoding steps needed to retrieve the unknown N - 1 [X'.sup.i.sub.L] received message packets at any user.
So, we need to retrieve the [X'.sup.i.sub.L] instead of the entire L packets, which means, that the number of the sequential network decoding steps decreased by N (L - 1) folders for the N users.
The above sequential network decoding steps at user k can be summarized by Equations (13) and (14), for the right and left branches respectively.
As in MSNC based on NC of bits independently per unit time setups, it is possible to reduce the number of the sequential network decoding steps by additionally transmitting CMPs [C.sub.T] as shown by Equations (15) and (16) for the kth user for the CPNC [AF.sub.p] system, and Equations (17) and (18) for [DF.sub.p], where Equations (15) and (17) are used to reduce the number of sequential network decoding steps needed in (13) and Equations (16) and (18) are used to reduce the number of sequential network decoding steps in (13) to retrieve the estimated CMPs at the left receiving side starting from [X'.sup.k-1.sub.L] to [X'.sup.1.sub.L].
Equations (15), (16), (17) and (18) show that, the number of possible additional transmitted CMPs is reduced by L - 1 folders as the total number of sequential network decoding steps reduced by L - 1 at first place.
So, instead of 9 sequential network decoding steps in MSNC, we need just 3 CPNC (taking into consideration that [X'.sup.k.sub.3], [X'.sup.k.sub.6], [X'.sup.k.sub.9] ...
In this paper, we propose a novel broadband CP antenna array utilizing Spidron fractal slots as radiating elements that are fed by parallel sequential networks. As discussed in Section 2, the single antenna element of the proposed array is comprehensively investigated in terms of its design considerations and operation principle.

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