16 research outputs found
Performance Analysis of Adaptive Physical Layer Network Coding for Wireless Two-way Relaying
The analysis of modulation schemes for the physical layer network-coded two
way relaying scenario is presented which employs two phases: Multiple access
(MA) phase and Broadcast (BC) phase. It was shown by Koike-Akino et. al. that
adaptively changing the network coding map used at the relay according to the
channel conditions greatly reduces the impact of multiple access interference
which occurs at the relay during the MA phase. Depending on the signal set used
at the end nodes, deep fades occur for a finite number of channel fade states
referred as the singular fade states. The singular fade states fall into the
following two classes: The ones which are caused due to channel outage and
whose harmful effect cannot be mitigated by adaptive network coding are
referred as the \textit{non-removable singular fade states}. The ones which
occur due to the choice of the signal set and whose harmful effects can be
removed by a proper choice of the adaptive network coding map are referred as
the \textit{removable} singular fade states. In this paper, we derive an upper
bound on the average end-to-end Symbol Error Rate (SER), with and without
adaptive network coding at the relay, for a Rician fading scenario. It is shown
that without adaptive network coding, at high Signal to Noise Ratio (SNR), the
contribution to the end-to-end SER comes from the following error events which
fall as : the error events associated with the removable
singular fade states, the error events associated with the non-removable
singular fade states and the error event during the BC phase. In contrast, for
the adaptive network coding scheme, the error events associated with the
removable singular fade states contributing to the average end-to-end SER fall
as and as a result the adaptive network coding scheme
provides a coding gain over the case when adaptive network coding is not used.Comment: 10 pages, 5 figure
Physical Layer Network Coding for Two-Way Relaying with QAM
The design of modulation schemes for the physical layer network-coded two way
relaying scenario was studied in [1], [3], [4] and [5]. In [7] it was shown
that every network coding map that satisfies the exclusive law is representable
by a Latin Square and conversely, and this relationship can be used to get the
network coding maps satisfying the exclusive law. But, only the scenario in
which the end nodes use -PSK signal sets is addressed in [7] and [8]. In
this paper, we address the case in which the end nodes use -QAM signal sets.
In a fading scenario, for certain channel conditions ,
termed singular fade states, the MA phase performance is greatly reduced. By
formulating a procedure for finding the exact number of singular fade states
for QAM, we show that square QAM signal sets give lesser number of singular
fade states compared to PSK signal sets. This results in superior performance
of -QAM over -PSK. It is shown that the criterion for partitioning the
complex plane, for the purpose of using a particular network code for a
particular fade state, is different from that used for -PSK. Using a
modified criterion, we describe a procedure to analytically partition the
complex plane representing the channel condition. We show that when -QAM () signal set is used, the conventional XOR network mapping fails to remove
the ill effects of , which is a singular fade state for
all signal sets of arbitrary size. We show that a doubly block circulant Latin
Square removes this singular fade state for -QAM.Comment: 13 pages, 14 figures, submitted to IEEE Trans. Wireless
Communications. arXiv admin note: substantial text overlap with
arXiv:1203.326
Distributed Space Time Coding for Wireless Two-way Relaying
We consider the wireless two-way relay channel, in which two-way data
transfer takes place between the end nodes with the help of a relay. For the
Denoise-And-Forward (DNF) protocol, it was shown by Koike-Akino et. al. that
adaptively changing the network coding map used at the relay greatly reduces
the impact of Multiple Access interference at the relay. The harmful effect of
the deep channel fade conditions can be effectively mitigated by proper choice
of these network coding maps at the relay. Alternatively, in this paper we
propose a Distributed Space Time Coding (DSTC) scheme, which effectively
removes most of the deep fade channel conditions at the transmitting nodes
itself without any CSIT and without any need to adaptively change the network
coding map used at the relay. It is shown that the deep fades occur when the
channel fade coefficient vector falls in a finite number of vector subspaces of
, which are referred to as the singular fade subspaces. DSTC
design criterion referred to as the \textit{singularity minimization criterion}
under which the number of such vector subspaces are minimized is obtained.
Also, a criterion to maximize the coding gain of the DSTC is obtained. Explicit
low decoding complexity DSTC designs which satisfy the singularity minimization
criterion and maximize the coding gain for QAM and PSK signal sets are
provided. Simulation results show that at high Signal to Noise Ratio, the DSTC
scheme provides large gains when compared to the conventional Exclusive OR
network code and performs slightly better than the adaptive network coding
scheme proposed by Koike-Akino et. al.Comment: 27 pages, 4 figures, A mistake in the proof of Proposition 3 given in
Appendix B correcte
Wireless Network-Coded Three-Way Relaying Using Latin Cubes
The design of modulation schemes for the physical layer network-coded
three-way wireless relaying scenario is considered. The protocol employs two
phases: Multiple Access (MA) phase and Broadcast (BC) phase with each phase
utilizing one channel use. For the two-way relaying scenario, it was observed
by Koike-Akino et al. \cite{KPT}, that adaptively changing the network coding
map used at the relay according to the channel conditions greatly reduces the
impact of multiple access interference which occurs at the relay during the MA
phase and all these network coding maps should satisfy a requirement called
\textit{exclusive law}. This paper does the equivalent for the three-way
relaying scenario. We show that when the three users transmit points from the
same 4-PSK constellation, every such network coding map that satisfies the
exclusive law can be represented by a Latin Cube of Second Order. The network
code map used by the relay for the BC phase is explicitly obtained and is aimed
at reducing the effect of interference at the MA stage.Comment: 13 Pages, 16 Figures. Some mistakes in the previous version have been
fixe
On Non-Binary Constellations for Channel Encoded Physical Layer Network Coding
This thesis investigates channel-coded physical layer network coding, in which the relay directly transforms the noisy superimposed channel-coded packets received from the two end nodes, to the network-coded combination of the source packets. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain each message explicitly at the relay. Here, the end nodes and choose their symbols, and , from a small non-binary field, , and use non-binary PSK constellation mapper during the transmission phase. The relay then directly decodes the network-coded combination over from the noisy superimposed channel-coded packets received from two end nodes. Trying to obtain and explicitly at the relay is overly ambitious when the relay only needs . For the binary case, the only possible network-coded combination, over the binary field, does not offer the best performance in several channel conditions. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients . As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of decoding coefficients. In this thesis, we compare different constellation mappers and prove that not all of them have distinct performance in terms of frame error rate. Moreover, we derive a lower bound on the frame error rate performance of decoding the network-coded combinations at the relay. Simulation results show that if we adopt concatenated Reed-Solomon and convolutional coding or low density parity check codes at the two end nodes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the frame error rate and, in particular, the ternary constellation has the best frame error rate performance among all considered cases