Error Rate Analysis of GF(q) Network Coded Detect-and-Forward Wireless Relay Networks Using Equivalent Relay Channel Models

This paper investigates simple means of analyzing the error rate performance of a general q-ary Galois Field network coded detect-and-forward cooperative relay network with known relay error statistics at the destination. Equivalent relay channels are used in obtaining an approximate error rate of the relay network, from which the diversity order is found. Error rate analyses using equivalent relay channel models are shown to be closely matched with simulation results. Using the equivalent relay channels, low complexity receivers are developed whose performances are close to that of the optimal maximum likelihood receiver.Comment: 28 pages, 10 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Anti error propagation methods for wireless uplink using network coding

Abstract—Wireless network coding suffers the error propaga-tion issues that may severely degrade the diversity performance. In this work, we develop two power scaling schemes at the relay side and two detection schemes at the receiver side, respectively, to mitigate error propagation in network-coded uplink channel and thus achieve full diversity. For the soft power scaling based link adaptive relaying, we develop a virtual channel model and demonstrate that the relay power should be such to balance the signal-to-noise ratios of the source-relay channel and relay-destination channel. As for the hard power scaling based ON-OFF relaying, we first design a decision rule based on total pairwise error probability, and then simplifies it to the threshold-based relaying strategy. At the receiver side, we show that the weighted minimum distance detection with the weight being determined by the relative link quality of source-relay channel and relay-destination channel can achieve full diversity once the global channel state information is available, otherwise the maximum likelihood detection that explicitly takes into account relay decoding error should be employed to achieve full diversity. I

On the Diversity Order and Coding Gain of Multi-Source Multi-Relay Cooperative Wireless Networks with Binary Network Coding

In this paper, a multi-source multi-relay cooperative wireless network with binary modulation and binary network coding is studied. The system model encompasses: i) a demodulate-and-forward protocol at the relays, where the received packets are forwarded regardless of their reliability; and ii) a maximum-likelihood optimum demodulator at the destination, which accounts for possible demodulations errors at the relays. An asymptotically-tight and closed-form expression of the end-to-end error probability is derived, which clearly showcases diversity order and coding gain of each source. Unlike other papers available in the literature, the proposed framework has three main distinguishable features: i) it is useful for general network topologies and arbitrary binary encoding vectors; ii) it shows how network code and two-hop forwarding protocol affect diversity order and coding gain; and ii) it accounts for realistic fading channels and demodulation errors at the relays. The framework provides three main conclusions: i) each source achieves a diversity order equal to the separation vector of the network code; ii) the coding gain of each source decreases with the number of mixed packets at the relays; and iii) if the destination cannot take into account demodulation errors at the relays, it loses approximately half of the diversity order.Comment: 35 pages, submitted as a Journal Pape

16-QAM Hierarchical Modulation Optimization in Relay Cooperative Networks

16-QAM Hierarchical Modulation Optimization in Relay Cooperative Networks Sara Sallam Recently, the concept of cooperative networks has attracted special attention in the field of wireless communications. This is due to their ability in achieving diversity with no extra hardware cost. The main drawback that characterizes cooperative networks is that they require extra transmission time slots compared to the traditional non-cooperative networks. Several strategies have been proposed in order to mitigate this disadvantage. One of the most recently adopted techniques is the use of hierarchical modulation. Hierarchical modulation was originally used in Digital Video Broadcast (DVB) applications. Lately, it has been applied in cooperative networks for its ability to transmit relative high data rate with acceptable performance. In this thesis, the application of a 4/16 QAM hierarchical modulation in cooperative networks is examined. This study focuses on a downlink cellular network scenario, composed of a Base Station, a Relay and two destinations. The Base Station intends to transmit two different streams of data to these two destinations by concatenating the two streams and broadcasting the resulting sequence using a non-uniform 4/16 QAM hierarchical modulation. Unlike previous work, the main contribution in this thesis is the optimization of the 16QAM constellation’s parameters according to each user’s channel condition. In other words, this method gives each user’s data the priority it needs in order to be detected as correctly as possible at the destination. Explicit closed form expressions of Hierarchical modulation Bit Error Rate in relay cooperative networks are derived. These BER expressions are used in order to select the constellation’s parameters that will achieve total minimum BER in coded and un-coded schemes. Results prove that the proposed method achieve noticeable improvement in both users performance compared to the use of uniform 16QAM constellation

Optimal Decoding and Performance analysis of a Noisy Channel Network with Network Coding

We investigate sink decoding approaches and performance analysis for a network with intermediate node encoding (coded network). The network consists of statistically independent noisy channels. The sink bit error probability (BEP) is the performance measure. First, we investigate soft-decision decoding without statistical information on the upstream channels (the channels not directly connected to the sink). Numerical results show that the decoder cannot significantly improve the performance from a hard-decision decoder. We develop union bounds for analysis. The bounds show the asymptotic (regarding SNR: signal-to-noise ratio) performance of the decoder. Using statistical information about the upstream channels, we can find the error patterns of final hop channels (channels directly connected to sinks).With the error patterns, maximum-likelihood (ML) decoding can be performed, and a significant improvement in the BEP is obtained. To evaluate the union bound for the ML decoder, we use an equivalent point procedure. It is reduced to the least-squares problem with a linear constraint in the medium-to-high SNR region. With deterministic knowledge of the errors in the upstream channels, a genie-aided decoder can further improve the performance. We give the union bound for the genie decoder, which is straightforward to evaluate. By analyzing these decoders, we find that knowledge about the upstream channels is essential for good sink decoding.© 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.QC 20111101. Updated from conference paper to articleVR Projec

Optimal Decoding and Performance analysis of a Noisy Channel Network with Network Coding

We investigate sink decoding approaches and performance analysis for a network with intermediate node encoding (coded network). The network consists of statistically independent noisy channels. The sink bit error probability (BEP) is the performance measure. First, we investigate soft-decision decoding without statistical information on the upstream channels (the channels not directly connected to the sink). Numerical results show that the decoder cannot significantly improve the performance from a hard-decision decoder. We develop union bounds for analysis. The bounds show the asymptotic (regarding SNR: signal-to-noise ratio) performance of the decoder. Using statistical information about the upstream channels, we can find the error patterns of final hop channels (channels directly connected to sinks).With the error patterns, maximum-likelihood (ML) decoding can be performed, and a significant improvement in the BEP is obtained. To evaluate the union bound for the ML decoder, we use an equivalent point procedure. It is reduced to the least-squares problem with a linear constraint in the medium-to-high SNR region. With deterministic knowledge of the errors in the upstream channels, a genie-aided decoder can further improve the performance. We give the union bound for the genie decoder, which is straightforward to evaluate. By analyzing these decoders, we find that knowledge about the upstream channels is essential for good sink decoding.© 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.QC 20111101. Updated from conference paper to articleVR Projec