Joint Network/Channel Decoding for Heterogeneous Multi-Source/Multi-Relay Cooperative Networks

Abstract

In this paper, we study joint network/channel decoding for multi-source multi-relay heterogeneous wireless networks. When convolutional and network codes are used at the physical and network layers, respectively, we show that error correction and diversity properties of the whole network can be characterized by an equivalent and distributed convolutional network/channel code. In particular, it is shown that, by properly choosing the network code, the equivalent code can show Unequal Error Protection (UEP) properties, which might be useful for heterogeneous wireless networks in which each source might ask for a different quality-ofservice requirement or error probability. Using this representation, we show that Maximum-Likelihood (ML) joint network/channel decoding can be performed by using the trellis representation of the distributed convolutional network/channel code. Furthermore, to deal with decoding errors at the relays, a ML-optimum receiver which exploits side information on the source-to-relay links is proposed.

Error Performance and Diversity Analysis of Multi-Source Multi-Relay Wireless Networks with Binary Network Coding and Cooperative MRC

“…The cases m = 0 and m = 2 NR − 1 can be obtained with similar analytical steps. Then, G ( ·| ·) in (14) can be re-written as shown in (32) at the top of this page, where: i) γ γ γ SRq is a short-hand to denote all channels from the N S sources to R q ; and ii) it is taken into account that d (m)…”

“…Then, G ( •| •) in ( 14) can be re-written as shown in (32) at the top of this page, where: i) γ γ γ SRq is a short-hand to denote all channels from the N S sources to R q ; and ii) it is taken into account that d Rq if µ q−1 = 1. To compute (32) in closed-form, the expectations Υ (•) and Γ (s) = NS t=1 g StRq Γ t (s) shown in (33) at the top of this page need to be studied. When computing Γ t (•), we assume g StRq = 1 as only in this case it contributes to Γ (•).…”

“…By using G ( •| •) in (32), the APEP (0 → c) in ( 14) can be re-written as shown in (45) at the top of this page, where: i) M1 ( s| c) = NS t=1 F t ( s| c); ii) M2 ( s| c, E m ) = NR q=1, µq−1=0 G q ( s| c, E m , µ q−1 = 0); and iii) M3 ( s| c, E m ) = NR q=1, µq−1=1 G q ( s| c, E m , µ q−1 = 1). From (45), APEP 0 → c(t) in ( 23) can be computed as: ≈ is obtained by applying the residues theorem [40, Eq.…”

“…Finally, by inserting (33)-( 35), (37), and (38) in (32), G ( •| •) in ( 14) can be obtained after some algebra and by taking into account that NR q=1, µq−1=0 1 − 4γ eqRq −1 → 1 for high-SNR. This concludes the proof.…”

“…Some preliminary Monte Carlo simulation results are available in [31]. Furthermore, recent simulation results including channel coding are available in [32]- [35]. In particular, recent results in [35] have shown that channel coding does not contribute to the diversity order of the sources if the channel is assumed to be quasi-static over all the wireless links.…”