Minimizing the average achievable distortion using multi-layer coding approach in two-hop networks

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Minimizing the average achievable distortion using multi-layer coding approach in two-hop networks Sayed Ali Khodam Hoseini1 · Soroush Akhlaghi1 · Mina Baghani1 Received: 17 July 2019 / Accepted: 12 September 2020 © Institut Mines-T´el´ecom and Springer Nature Switzerland AG 2020

Abstract Minimizing the average achievable distortion (AAD) of a Gaussian source at the destination of a two-hop block fading relay channel is studied in this paper. The communication is carried out through the use of a Decode and Forward (DF) relay with no source-destination direct links. The associated receivers of both hops are assumed to be aware of the corresponding channel state information (CSI), while the transmitters are unaware of their corresponding CSI. The current paper explores the effectiveness of incorporating the successive refinement source coding together with multi-layer channel coding in minimizing the AAD. In this regard, the closed form and optimal power allocation policy across code layers of the second hop is derived, and using a proper curve fitting approach, a close-to-optimal power allocation policy associated with the first hop is devised. It is numerically shown that the DF strategy closely follows the Amplify and Forward (AF) relaying, while there is a sizable gap between the AAD of multi-layer coding and single-layer source coding. Keywords Multi-layer coding · Broadcast approach · Source coding · Rate-distortion theory · Relay-assisted channels · Calculus of variations

1 Introduction Quality of service assurance is a critical key performance indicator (KPI) in wireless networks where relaying is a promising approach to improve it [1, 2]. In this regard, the Decode-and-Forward (DF) and the Amplify-andForward (AF) protocols have widely gained interest [3–6]. It is demonstrated that employing DF strategy in a relayassisted network maximizes the achievable rate, when there is not any direct link between the transmission ends [2]. The instantaneous channel state information at the transmitter (CSIT) is a crucial factor for adapting the transmission rate in wireless channels, while it is not possible to have CSIT in certain applications. The  Soroush Akhlaghi

[email protected] Sayed Ali Khodam Hoseini [email protected] Mina Baghani [email protected] 1

Department of Electrical Engineering, Shahed University, Tehran, Iran

outage approach is the traditional way to cope with this situation, which consists of the single-layer transmission corresponding to a fixed channel strength threshold. In this case, a number of transmissions would not be successful according to the channel fading statistics. Multilayer coding is an alternative approach under which the point-to-point channel is thought as a point-to-multi point (broadcast) channel with virtual receivers, each corresponding to a channel realization. Accordingly, the optimal power assignment across code layers is devised at [7, 8]. Since then, there have been various conditions in which the multi-layer coding is addressed. Finding the power all