Network Coding Modulation Research Articles

Trellis- and Network-Coded Modulation for Decode-and-Forward Two-Way Relaying Over Time-Varying Channels

We present a bandwidth-efficient joint channel coding-modulation scheme conceived for the broadcast channel of decode-and-forward (DF) two-way relaying (TWR), where trellis-coded modulation (TCM) is intrinsically amalgamated with network-coded modulation (NCM) for achieving both a channel coding gain and a high throughput. We conceive a low-complexity receiver algorithm for our joint TC-NCM scheme, which applies decoding and demodulation simultaneously, without the need to first demodulate the signal before decoding, as in the traditional solutions. As a further contribution, the TC-NCM scheme is intrinsically amalgamated with adaptive transceiver techniques. We then further investigate the performance of our near-instantaneously adaptive discrete-rate TC-NC-quadrature-amplitude modulation/phase-shift keying (QAM-PSK) scheme. Both simulation results and numerical analysis are presented, which are compared with the performance of traditional NCM schemes. The results show that our scheme not only increases the achievable transmission rate but improves the reliability as well, yet it is of modest complexity.

Analog Network-Coded Modulation With Maximum Euclidean Distance: Mapping Criterion and Constellation Design

Physical-layer network coding holds the great potential of improving the power efficiency and the spectral efficiency for the two-stage transmission scheme. The first stage is the multiple access stage, where two source nodes (SN1 and SN2) simultaneously transmit to the relay node (RN). The second stage is the Broadcast stage, where the RN broadcasts to the two destination nodes (DN1 and DN2), after a denoising-and-mapping operation. In this paper, we investigate the joint network-coded modulation design of the two stages. A universal modulation framework is built, referred to as analog network-coded modulation strategy, which is more general than the former modulation design mechanism. More explicitly, we propose a joint design criterion to guarantee the forwarding reliability at the RN. The criterion ensures that the neighboring constellation points superposed at the RN are mapped to an identical constellation point for broadcasting if their Euclidean distance (ED) is less than a given threshold. This yields a non-convex polynomial optimization problem by minimizing the average transmission power and constraining the ED among the constellation points. By solving the problem, we propose two joint modulation design algorithms, termed as the Enhanced Semidefinite Relaxation Algorithm and the Fast-Relaxation Algorithm, respectively. The two algorithms can achieve the tradeoff between the communication performance and the computation resources. As for the Fast-Relaxation Algorithm, the theoretical performance boundary is derived in detail. Simulation results demonstrate the effectiveness of both the proposed algorithms by comparing symbol error rate performance with the existing modulation design methods.

Truncated-ARQ Aided Adaptive Network Coding for Cooperative Two-Way Relaying Networks: Cross-Layer Design and Analysis

Network Coding (NC) constitutes a promising technique of improving the throughput of relay-aided networks. In this context, we propose a cross-layer design for both amplifyand- forward (AF-) and decode-and-forward two-way relaying (DF-TWR) based on the NC technique invoked for improving the achievable throughput under specific Quality of Service (QoS) requirements, such as the maximum affordable delay and error rate.We intrinsically amalgamate adaptive Analog Network Coding (ANC) and Network Coded Modulation (NCM) with truncated Automatic Repeat reQuest (ARQ) operating at the different OSI layers. At the data-link layer, we design a pair of improved NC-based ARQ strategies based on the Stop-andwait and the Selective-repeat ARQ protocols. At the physical layer, adaptive ANC/NCM are invoked based on our approximate packet error ratio (PER). We demonstrate that the adaptive ANC design can be readily amalgamated with the proposed protocols. However, adaptive NC-QAM suffers from an SNR-loss, when the transmit rates of the pair of downlink (DL) channels spanning from the relay to the pair of destinations are different. Therefore we develop a novel transmission strategy for jointly selecting the optimal constellation sizes for both of the relay-to-destination links that have to be adapted to both pair of channel conditions. Finally, we analyze the attainable throughput, demonstrating that our truncated ARQ-aided adaptive ANC/NCM schemes attain considerable throughput gains over the schemes dispensing with ARQ, whilst our proposed scheme is capable of supporting bidirectional NC scenarios.

Hierarchical Pairwise Error Probability for Hierarchical Decode and Forward Strategy in PLNC

Pairwise error probability (PEP) is an essential tool allowing to design practical optimized coding schemes. It reveals the connection between the performance and the decoding metric that is directly related to the codeword and/or constellation properties. The application of this principle to the hierarchical PEP used to describe the decoding performance of many-to-one message functions (hierarchical network code maps) in physical layer network coding (PLNC) is addressed in this letter. Unlike for the single-user case, the hierarchical PEP reveals a complicated dependence on the structure of the hierarchical codeword/constellation. The structure is defined in terms of hierarchical distance and hierarchical self-distance spectra . We show that the network coded modulation (NCM) minimizing the hierarchical decoding error probability should have zero self-distance spectrum leading to self-folded NCM design criterion .

Hierarchical Network Transfer Function and Doubly-Greedy Half-Duplex Stage Scheduling for WPNC Networks

Wireless Physical Layer Network Coding (WPNC) based communication networks deliver the information from sources to destinations through the complex relay network. To properly design the Network Coded Modulation transmitted by network nodes and the relay processing including the Hierarchical Network Code (HNC) maps, we need a formal description of the global network processing function. Any practical implementation also implies the half-duplex constrained relays which imposes the network to work in multiple stages. We present a polynomial based formalism defining the Hierarchical Network Transfer Function (H-NTF). It captures all phenomena related to the stage dependent transmit and receive activity over the network, including potential buffering, and mainly the hierarchy of forming the local HNC maps into the global hierarchical flow description. Using the polynomial formalism of H-NTF, we develop the half-duplex constrained stage scheduling algorithm. It starts with finding a causal minimal latency (or close to minimal) critical sequence with subsequent doubly (first Rx then Tx) greedy mapping of the node activity compliant with the half-duplex constraint.

Variable-Rate, Variable-Power Network-Coded-QAM/PSK for Bi-Directional Relaying Over Fading Channels

Network coded modulation (NCM) holds the promise of significantly improving the efficiency of two-way wireless relaying. In this contribution, we propose near instantaneously adaptive variable-rate, variable-power QAM/PSK for NC-aided decode-and-forward two-way relaying (DF-TWR) to maximize the average throughput. The proposed scheme is optimized subject to both average-power and bit-error-ratio (BER) constraints. Based on the BER bounds, we investigate a discrete-rate adaptation scheme, relying on a pair of solutions proposed for maximizing the spectral efficiency of the network. We then derive a closed-form solution based power adaptation policy for a continuous-rate scheme and quantify the signal-to-noise ratio (SNR) loss imposed by NC-QAM. Our simulation results demonstrate that the proposed discrete adaptive NC-QAM/PSK schemes are capable of attaining a higher spectral efficiency than their fixed-power counterparts.

Maximum Euclidean distance network coded modulation for asymmetric decode‐and‐forward two‐way relaying

Network coding (NC) compresses two traffic flows with the aid of low-complexity algebraic operations, hence holds the potential of significantly improving both the efficiency of wireless two-way relaying, where each receiver is collocated with a transmitter and hence has prior knowledge of the message intended for the distant receiver. In this contribution, network coded modulation (NCM) is proposed for jointly performing NC and modulation. As in classic coded modulation, the Euclidean distance between the symbols is maximised, hence the symbol error probability is minimised. Specifically, the authors first propose set-partitioning-based NCM as an universal concept which can be combined with arbitrary constellations. Then the authors conceive practical phase-shift keying/quadrature amplitude modulation (PSK/QAM) NCM schemes, referred to as network coded PSK/QAM, based on modulo addition of the normalised phase/amplitude. To achieve a spatial diversity gain at a low complexity, a NC oriented maximum ratio combining scheme is proposed for combining the network coded signal and the original signal of the source. An adaptive NCM is also proposed to maximise the throughput while guaranteeing a target bit error probability (BEP). Both theoretical performance analysis and simulations demonstrate that the proposed NCM can achieve at least 3 dB signal-to-noise ratio gain and two times diversity gain.

Network Coded Modulation for Random Channel Class in WNC with HDF Relaying Strategy

A standard NCM (Network Coded Modulation) for WNC (Wireless Network Coding) with HDF (Hierarchical Decode & Forward) strategy requires that each node has full knowledge of the connectivity pattern to other nodes and this knowledge affects the design of NCM and HNC (Hierarchical Network Code) maps at each transmitting (source) and receiving (relay) node respectively. The final destination has to have full knowledge of all HNC maps used and the composite overall HNC map needs to be invertible to recover the source data. This approach collapses if nodes do not have a full knowledge of the connectivity pattern and thus cannot adjust their HNC maps properly. We design the NCM and HNC maps for WNC with HDF strategy that works regardless of this knowledge. It is based on a concept of a channel class which is a discrete (random) parameter describing the channel behavior and which becomes a part of HNC maps and the NCM hierarchical constellation. We analyze the rate regions for this design and compare it to the standard NCM and HNC map solution suffering from random channel outages.

Performance Comparison of Two Network Coding Modulation Scheme in Multiple Access Relay Cooperation

In this paper, two different modulation schemes are developed in multiple access relay cooperation with network coding. Performance analysis and simulation results show that there is one point where the two modulation schemes have the same system outage probability. This finding can be utilized to propose an adaptive modulation scheme.

Design Criteria for Hierarchical Exclusive Code with Parameter-Invariant Decision Regions for Wireless 2-Way Relay Channel

The unavoidable parametrization of the wireless link represents a major problem of the network-coded modulation synthesis in a 2-way relay channel. Composite (hierarchical) codeword received at the relay is generally parametrized by the channel gain, forcing any processing on the relay to be dependent on channel parameters. In this paper, we introduce the codebook design criteria, which ensure that all permissible hierarchical codewords have decision regions invariant to the channel parameters (as seen by the relay). We utilize the criterion for parameter-invariant constellation space boundary to obtain the codebooks with channel parameter-invariant decision regions at the relay. Since the requirements on such codebooks are relatively strict, the construction of higher-order codebooks will require a slightly simplified design criteria. We will show that the construction algorithm based on these relaxed criteria provides a feasible way to the design of codebooks with arbitrary cardinality. The promising performance benefits of the example codebooks (compared to a classical linear modulation alphabets) will be exemplified on the minimum distance analysis.