# Theoretical results update of assessment on feasibility, achievability, and limits : ICT-619555 RESCUE D1.2.2 Version 1.0

##### He, Jiguang; Tervo, Valtteri; Yi, Na; Hou, Jiancao; He, Xin; Qian, Shen; Matsumoto, Tad; Wolf, Albrecht (2016-09-16)

He, Jiguang; Tervo, Valtteri; Yi, Na; Hou, Jiancao; He, Xin; Qian, Shen; Matsumoto, Tad; Wolf, Albrecht (2016) Theoretical results update of assessment on feasibility, achievability, and limits : ICT-619555 RESCUE D1.2.2 Version 1.0. pp. 1-83

This material is posted here by permission of the EU FP7 RESCUE Project. http://www.ict-rescue.eu/ RESCUE is founded by the European Commission under the 7th Framework Programme,Theme 3- "ICT"call FP7-ICT-2013-11,Work Programme Topic 1.1"Future Networks"

https://rightsstatements.org/vocab/InC/1.0/

**Julkaisun pysyvä osoite on**

https://urn.fi/URN:NBN:fi-fe201703011908

##### Tiivistelmä

Abstract

Compared to the intermediate deliverable D1.2.1, additional results regarding the achievable rate region and performance limit analyses for different toy scenarios (TSs) have been achieved, which are provided in this deliverable. For TS1, we investigate the impact of the line-of-sight component on outage probability with lossy forwarding strategy. Moreover, an improved selective decode-and-forward scheme with least square based symbol level filtering is proposed in order to improve the bit error rate performance of the relaying system. Regarding TS2, the lower bound of the Hamming distortion in the binary chief executive officer (CEO) problem is derived by minimizing the distortion function subject to the inequalities between the obtained tighter outer bound and the channel capacities. An extension to an arbitrary number of sources in the CEO problem is also studied. TS3 is modeled by Slepian-Wolf coding, and we achieve the upper bound of the outage probability by reducing and relaxing the rate constraints. Regarding TS4, we extend the orthogonal transmission to its non-orthogonal counterpart and analyze the outage probability relying on the theorem of multiple access channel with a helper.

Executive summary

Compared to the intermediate deliverable D1.2.1, this deliverable presents some additional theoretical results regarding the achievable rate regions and performance limits on the links-on-the-fly concept introduced in “Links-onthe-fly Technology for Robust, Efficient, and Smart Communication in Unpredictable Environments” (RESCUE) project. As in D1.2.1, all the theoretical results are obtained based on the simplified four toy scenarios (TSs), where the relays always forward their decoded information sequence to the destination ignoring whether it contains error or not. The advantages of the links-on-the-fly concept over its baseline schemes have been extensively studied and investigated in D1.2.1. Therefore, in this deliverable we mainly focus on the theoretical results of the links-on-the-fly concept by making some scenario extensions and generalizations.

Toy Scenario 1 (TS1) is a typical three-node one-way relay network. The achievable rate region of TS1 was studied in D1.2.1 based on the theorem of source coding with a helper and approximated by the Slepian-Wolf theorem. All the links are supposed to be independent and identically distributed (i.i.d) Rayleigh block fading without considering line-of-sight component. We further extend the wireless channels to i.i.d Rician and Nakagami-m fading and calculate the theoretical outage probability of TS1. In addition, the Kullback-Leibler distance between the Rician and Nakagami-m fading distributions is studied, which in turn provides the guideline for the analysis of diversity and coding gains shown in the theoretical outage probability. A more advanced lossy forwarding1 scheme with least square based symbol level filtering is investigated over TS1, which guarantees better bit error rate (BER) performance compared to the baselines.

Toy scenario 2 (TS2) is a single-source multiple-relays and single-destination system without direct link between the source and the destination. As in D1.2.1, we mainly focus on the chief executive officer (CEO) problem, which results from the special case where all the source-to-relay links are lossy. We first reduce the binary CEO problem to a binary multiterminal source coding problem. Then, we derive the tighter outer bound on the rate distortion region for the binary multiterminal source coding problem based on the converse proof of the bound. Furthermore, a lower bound on the Hamming distortion for the CEO problem is obtained by minimizing the distortion function subject to the inequalities between the derived outer bound and the channel capacities. Finally, an extension of the binary CEO problem to an arbitrary number of terminals is investigated. The correctness/accuracy of the derivations is also verified through practical simulations using accumulator (ACC) aided turbo codes.

Toy scenario 3 (TS3) is an extension of TS2 with direct link between the source and the destination. In the D1.2.1, the selective DF was intensively investigated. Here, we analyze the upper bound of the outage probability by reducing and relaxing the rate constraints based on Slepian-Wolf theorem. Closed form expression for the outage probability is derived for the high signal to noise ratio (SNR) regime with up to four relays. Comparison between the cases with different number of relays is carried out to show the improved diversity order when the number of relays increases.

Toy scenario 4 (TS4) is a multiple access relay channel (MARC) with two sources, single relay and a common destination. The achievable rate region and outage probability was intensively studied in D1.2.1 under the constraint of perfect or imperfect source-to-relay links and orthogonal transmission. We relax the restriction on the assumption of orthogonal transmission and apply the non-orthogonal transmission to MARC. A virtual channel between the source-to-relay links is established for the purpose of simplifying the analysis. The achievable rate region is further obtained by the theorem of multiple access channel with a helper, which determines the outage probability. The outage probability of non-orthogonal MARC is slightly worse than orthogonal MARC, but the time slot consumption for the data transmission between sources and destination is reduced considerably.

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