Decoding Strategies at the Relay with Physical-Layer Network Coding

Cataloged from PDF version of article.A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large

Iterative decoding and detection for physical layer network coding

PhD ThesisWireless networks comprising multiple relays are very common and it is important that all users are able to exchange messages via relays in the shortest possible time. A promising technique to achieve this is physical layer network coding (PNC), where the time taken to exchange messages between users is achieved by exploiting the interference at the relay due to the multiple incoming signals from the users. At the relay, the interference is demapped to a binary sequence representing the exclusive-OR of both users’ messages. The time to exchange messages is reduced because the relay broadcasts the network coded message to both users, who can then acquire the desired message by applying the exclusive-OR of their original message with the network coded message. However, although PNC can increase throughput it is at the expense of performance degradation due to errors resulting from the demapping of the interference to bits. A number of papers in the literature have investigated PNC with an iterative channel coding scheme in order to improve performance. However, in this thesis the performance of PNC is investigated for end-to-end (E2E) the three most common iterative coding schemes: turbo codes, low-density parity-check (LDPC) codes and trellis bit-interleaved coded modulation with iterative decoding (BICM-ID). It is well known that in most scenarios turbo and LDPC codes perform similarly and can achieve near-Shannon limit performance, whereas BICM-ID does not perform quite as well but has a lower complexity. However, the results in this thesis show that on a two-way relay channel (TWRC) employing PNC, LDPC codes do not perform well and BICM-ID actually outperforms them while also performing comparably with turbo codes. Also presented in this thesis is an extrinsic information transfer (ExIT) chart analysis of the iterative decoders for each coding scheme, which is used to explain this surprising result. Another problem arising from the use of PNC is the transfer of reliable information from the received signal at the relay to the destination nodes. The demapping of the interference to binary bits means that reliability information about the received signal is lost and this results in a significant degradation in performance when applying soft-decision decoding at the destination nodes. This thesis proposes the use of traditional angle modulation (frequency modulation (FM) and phase modulation (PM)) when broadcasting from the relay, where the real and imaginary parts of the complex received symbols at the relay modulate the frequency or phase of a carrier signal, while maintaining a constant envelope. This is important since the complex received values at the relay are more likely to be centred around zero and it undesirable to transmit long sequences of low values due to potential synchronisation problems at the destination nodes. Furthermore, the complex received values, obtained after angle demodulation, are used to derive more reliable log-likelihood ratios (LLRs) of the received symbols at the destination nodes and consequently improve the performance of the iterative decoders for each coding scheme compared with conventionally coded PNC. This thesis makes several important contributions: investigating the performance of different iterative channel coding schemes combined with PNC, presenting an analysis of the behaviour of different iterative decoding algorithms when PNC is employed using ExIT charts, and proposing the use of angle modulation at the relay to transfer reliable information to the destination nodes to improve the performance of the iterative decoding algorithms. The results from this thesis will also be useful for future research projects in the areas of PNC that are currently being addressed, such as synchronisation techniques and receiver design.Iraqi Ministry of Higher Education and Scientific Research

On Code Design for Interference Channels

abstract: There has been a lot of work on the characterization of capacity and achievable rate regions, and rate region outer-bounds for various multi-user channels of interest. Parallel to the developed information theoretic results, practical codes have also been designed for some multi-user channels such as multiple access channels, broadcast channels and relay channels; however, interference channels have not received much attention and only a limited amount of work has been conducted on them. With this motivation, in this dissertation, design of practical and implementable channel codes is studied focusing on multi-user channels with special emphasis on interference channels; in particular, irregular low-density-parity-check codes are exploited for a variety of cases and trellis based codes for short block length designs are performed. Novel code design approaches are first studied for the two-user Gaussian multiple access channel. Exploiting Gaussian mixture approximation, new methods are proposed wherein the optimized codes are shown to improve upon the available designs and off-the-shelf point-to-point codes applied to the multiple access channel scenario. The code design is then examined for the two-user Gaussian interference channel implementing the Han-Kobayashi encoding and decoding strategy. Compared with the point-to-point codes, the newly designed codes consistently offer better performance. Parallel to this work, code design is explored for the discrete memoryless interference channels wherein the channel inputs and outputs are taken from a finite alphabet and it is demonstrated that the designed codes are superior to the single user codes used with time sharing. Finally, the code design principles are also investigated for the two-user Gaussian interference channel employing trellis-based codes with short block lengths for the case of strong and mixed interference levels.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Iterative decoding combined with physical-layer network coding on impulsive noise channels

PhD ThesisThis thesis investigates the performance of a two-way wireless relay channel (TWRC) employing physical layer network coding (PNC) combined with binary and non-binary error-correcting codes on additive impulsive noise channels. This is a research topic that has received little attention in the research community, but promises to offer very interesting results as well as improved performance over other schemes. The binary channel coding schemes include convolutional codes, turbo codes and trellis bitinterleaved coded modulation with iterative decoding (BICM-ID). Convolutional codes and turbo codes defined in finite fields are also covered due to non-binary channel coding schemes, which is a sparse research area. The impulsive noise channel is based on the well-known Gaussian Mixture Model, which has a mixture constant denoted by α. The performance of PNC combined with the different coding schemes are evaluated with simulation results and verified through the derivation of union bounds for the theoretical bit-error rate (BER). The analyses of the binary iterative codes are presented in the form of extrinsic information transfer (ExIT) charts, which show the behaviour of the iterative decoding algorithms at the relay of a TWRC employing PNC and also the signal-to-noise ratios (SNRs) when the performance converges. It is observed that the non-binary coding schemes outperform the binary coding schemes at low SNRs and then converge at higher SNRs. The coding gain at low SNRs become more significant as the level of impulsiveness increases. It is also observed that the error floor due to the impulsive noise is consistently lower for non-binary codes. There is still great scope for further research into non-binary codes and PNC on different channels, but the results in this thesis have shown that these codes can achieve significant coding gains over binary codes for wireless networks employing PNC, particularly when the channels are harsh

Efficient Transmission Techniques in Cooperative Networks: Forwarding Strategies and Distributed Coding Schemes

This dissertation focuses on transmission and estimation schemes in wireless relay network, which involves a set of source nodes, a set of destination nodes, and a set of nodes helps communication between source nodes and destination nodes, called relay nodes. It is noted that the overall performance of the wireless relay systems would be impacted by the relay methods adopted by relay nodes. In this dissertation, efficient forwarding strategies and channel coding involved relaying schemes in various relay network topology are studied.First we study a simple structure of relay systems, with one source, one destination and one relay node. By exploiting “analog codes” -- a special class of error correction codes that can directly encode and protect real-valued data, a soft forwarding strategy –“analog-encode-forward (AEF)”scheme is proposed. The relay node first soft-decodes the packet from the source, then re-encodes this soft decoder output (Log Likelihood Ratio) using an appropriate analog code, and forwards it to the destination. At the receiver, both a maximum-likelihood (ML) decoder and a maximum a posterior (MAP) decoder are specially designed for the AEF scheme.The work is then extended to parallel relay networks, which is consisted of one source, one destination and multiple relay nodes. The first question confronted with us is which kind of soft information to be relayed at the relay nodes. We analyze a set of prevailing soft information for relaying considered by researchers in this field. A truncated LLR is proved to be the best choice, we thus derive another soft forwarding strategy – “Z” forwarding strategy. The main parameter effecting the overall performance in this scheme is the threshold selected to cut the LLR information. We analyze the threshold selection at the relay nodes, and derive the exact ML estimation at the destination node. To circumvent the catastrophic error propagation in digital distributed coding scheme, a distributed soft coding scheme is proposed for the parallel relay networks. The key idea is the exploitation of a rate-1 soft convolutional encoder at each of the parallel relays, to collaboratively form a simple but powerful distributed analog coding scheme. Because of the linearity of the truncated LLR information, a nearly optimal ML decoder is derived for the distributed coding scheme. In the last part, a cooperative transmission scheme for a multi-source single-destination system through superposition modulation is investigated. The source nodes take turns to transmit, and each time, a source “overlays” its new data together with (some or all of) what it overhears from its partner(s), in a way similar to French-braiding the hair. We introduce two subclasses of braid coding, the nonregenerative and the regenerative cases, and, using the pairwise error probability (PEP) as a figure of merit, derive the optimal weight parameters for each one. By exploiting the structure relevance of braid codes with trellis codes, we propose a Viterbi maximum-likelihood (ML) decoding method of linear-complexity for the regenerative case. We also present a soft-iterative joint channel-network decoding. The overall decoding process is divided into the forward message passing and the backward message passing, which makes effective use of the available reliability information from all the received signals. We show that the proposed “braid coding” cooperative scheme benefits not only from the cooperative diversity but also from the bit error rate (BER) performance gain

Relay Selection with Network Coding in Two-Way Relay Channels

In this paper, we consider the design of joint network coding (NC)and relay selection (RS) in two-way relay channels. In the proposed schemes, two users first sequentially broadcast their respective information to all the relays. We propose two RS schemes, a single relay selection with NC and a dual relay selection with NC. For both schemes, the selected relay(s) perform NC on the received signals sent from the two users and forward them to both users. The proposed schemes are analyzed and the exact bit error rate (BER) expressions are derived and verified through Monte Carlo simulations. It is shown that the dual relay selection with NC outperforms other considered relay selection schemes in two-way relay channels. The results also reveal that the proposed NC relay selection schemes provide a selection gain compared to a NC scheme with no relay selection, and a network coding gain relative to a conventional relay selection scheme with no NC.Comment: 11 pages, 5 figure

Analysis of hybrid-ARQ based relaying protocols under modulation constraints

In a seminal paper published in 2001, Caire and Tuninetti derived an information theoretic bound on the throughput of hybrid-ARQ in the presence of block fading. However, the results placed no constraints on the modulation used, and therefore the input to the channel was Gaussian. The purpose of this thesis is to investigate the impact of modulation constraints on the throughput of hybrid-ARQ in a block fading environment. First, we consider the impact of modulation constraints on information outage probability for a block fading channel with a fixed length codeword. Then, we consider the effect of modulation constraints upon the throughput of hybrid-ARQ, where the rate of the codeword varies depending on the instantaneous channel conditions. These theoretical bounds are compared against the simulated performance of HSDPA, a newly standardized hybrid-ARQ protocol that uses QPSK and 16-QAM bit interleaved turbo-coded modulation. The results indicate how much of the difference between HSDPA and the previous unconstrained modulation bound is due to the use of the turbo-code and how much is due to the modulation constraints. (Abstract shortened by UMI.)

Coherent and Non-coherent Techniques for Cooperative Communications

Future wireless network may consist of a cluster of low-complexity battery-powered nodes or mobile stations (MS). Information is propagated from one location in the network to another by cooperation and relaying. Due to the channel fading or node failure, one or more relaying links could become unreliable during multiple-hop relaying. Inspired by conventional multiple-input multiple-output (MIMO) techniques exploiting multiple co-located transmit antennas to introduce temporal and spatial diversity, the error performance and robustness against channel fading of a multiple-hop cooperative network could be significantly improved by creating a virtual antenna array (VAA) with various distributed MIMO techniques. In this thesis, we concentrate on the low-complexity distributed MIMO designed for both coherent and non-coherent diversity signal reception at the destination node. Further improvement on the network throughput as well as spectral efficiency could be achieved by extending the concept of unidirectional relaying to bidirectional cooperative communication. Physical-layer network coding (PLNC) assisted distributed space-time block coding (STBC) scheme as well as non-coherent PLNC aided distributed differential STBC system are proposed. It is confirmed by the theoretical analysis that both approaches have the potential for offering full spatial diversity gain. 　　 Furthermore, differential encoding and non-coherent detection techniques are generally associated with performance degradation due to the doubled noise variance. More importantly, conventional differential schemes suffer from the incapability of recovering the source information in time-varying channels owing to the assumption of static channel model used in the derivation of non-coherent detection algorithm. Several low-complexity solutions are proposed and studied in this thesis, which are able to compensate the performance loss caused by non-coherent detection and guarantee the reliable recovery of information in applications with high mobility. A substantial amount of iteration gain is achieved by combining the differential encoding with error-correction code and sufficient interleaving, which allows iterative possessing at the receiver