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Preface; Contents; 1 Coding Techniques for Transmitting Packets Through Complex Communication Networks; 1.1 Introduction; 1.2 Gabidulin Codes; 1.2.1 Decoding Using the Linearized Extended Euclidean Algorithm (LEEA); 1.2.2 Linearized Shift-Register Synthesis; 1.2.3 Remarks; 1.3 Interleaved Gabidulin Codes; 1.3.1 Decoding Interleaved Gabidulin Codes; 1.3.2 Remarks; 1.4 Partial Unit Memory Codes; 1.4.1 Convolutional Codes; 1.4.2 (Partial) Unit Memory Codes; 1.4.3 Distance Measures; 1.4.4 Upper Bounds; 1.4.5 Construction; 1.4.6 Calculation of Distances; 1.4.7 Remarks; 1.5 Bounds for List Decoding
1.5.1 Subspace Codes1.5.2 Constant-Rank Codes; 1.5.3 Constant-Dimension and Constant-Rank Codes; 1.5.4 Constant-Dimension Codes from Lifted MRD Codes; 1.5.5 Connection Between Constant-Rank Codes and List Size; 1.5.6 Upper Bound on the List Size; 1.5.7 Lower Bound on the List Size; 1.5.8 Interpretation and Conclusion; 1.5.9 Remarks; References; 2 Modulo-Type Precoding for Networks; 2.1 Introduction; 2.1.1 MIMO Broadcast Channel; 2.1.2 Finite-Field Matrix Channels; 2.1.3 Analogies and Dualities; 2.2 Connection Between Complex-Valued and Finite-Field Channels in Precoding
2.2.1 Conventional Schemes2.2.2 Lattice-Reduction-Aided Schemes; 2.2.3 Integer-Forcing Schemes; 2.2.4 Summary; 2.3 Precoding for Distributed MIMO; 2.3.1 Optimization Under Per-Antenna Power Constraints; 2.3.2 Coordination Effort and Hierarchical Precoding; 2.3.3 Selection of the Coordination Strategy; 2.3.4 Quantization of Precoded Symbols; 2.4 Precoding for Finite-Field Channels; 2.4.1 Differential Linear Network Coding; 2.4.2 Selection Precoding; References; 3 Enabling the Multi-User Generalized Degrees of Freedom in Cellular Interference Networks with Multi-User Coding; 3.1 Introduction
3.1.1 Road to Constant-Gap Sum-Capacity Approximations of Cellular Channels3.2 The Interfering Multiple Access Channel; 3.3 Linear Deterministic Approximation of the IMAC in the Weak Interference Regime; 3.3.1 Approximate Sum-Capacity; 3.3.2 Duality Between IMAC and IBC; 3.3.3 Transfer to the Gaussian IMAC; 3.4 Lower Triangular Deterministic Model; 3.4.1 Approximate Sum-Capacity; 3.5 Discussion; References; 4 The Information-Theoretic Constant-Gap Optimality of Treating Interference as Noise in Interference Networks; 4.1 Introduction; 4.2 Optimality of Treating Interference as Noise
4.2.1 GDOF Perspective4.2.2 Finite SNR Regime; 4.3 Approximate Optimality; 4.3.1 System Model; 4.3.2 Simple Interference Management in PIMAC; 4.3.3 Upper Bound for the Capacity of the PIMAC; 4.3.4 GDoF Optimality of Simple Schemes; 4.4 Constant Gap Analysis; 4.5 TIN Is Always Sub-optimal; 4.6 Summary; References; 5 Interference-Aware Analog Computation over the Wireless Channel: Fundamentals and Strategies; 5.1 Introduction; 5.1.1 Related Work; 5.1.2 Notation; 5.2 Communication Versus Computation; 5.2.1 The Wireless Multiple-Access Channel; 5.2.2 The Communication Problem
1.5.1 Subspace Codes1.5.2 Constant-Rank Codes; 1.5.3 Constant-Dimension and Constant-Rank Codes; 1.5.4 Constant-Dimension Codes from Lifted MRD Codes; 1.5.5 Connection Between Constant-Rank Codes and List Size; 1.5.6 Upper Bound on the List Size; 1.5.7 Lower Bound on the List Size; 1.5.8 Interpretation and Conclusion; 1.5.9 Remarks; References; 2 Modulo-Type Precoding for Networks; 2.1 Introduction; 2.1.1 MIMO Broadcast Channel; 2.1.2 Finite-Field Matrix Channels; 2.1.3 Analogies and Dualities; 2.2 Connection Between Complex-Valued and Finite-Field Channels in Precoding
2.2.1 Conventional Schemes2.2.2 Lattice-Reduction-Aided Schemes; 2.2.3 Integer-Forcing Schemes; 2.2.4 Summary; 2.3 Precoding for Distributed MIMO; 2.3.1 Optimization Under Per-Antenna Power Constraints; 2.3.2 Coordination Effort and Hierarchical Precoding; 2.3.3 Selection of the Coordination Strategy; 2.3.4 Quantization of Precoded Symbols; 2.4 Precoding for Finite-Field Channels; 2.4.1 Differential Linear Network Coding; 2.4.2 Selection Precoding; References; 3 Enabling the Multi-User Generalized Degrees of Freedom in Cellular Interference Networks with Multi-User Coding; 3.1 Introduction
3.1.1 Road to Constant-Gap Sum-Capacity Approximations of Cellular Channels3.2 The Interfering Multiple Access Channel; 3.3 Linear Deterministic Approximation of the IMAC in the Weak Interference Regime; 3.3.1 Approximate Sum-Capacity; 3.3.2 Duality Between IMAC and IBC; 3.3.3 Transfer to the Gaussian IMAC; 3.4 Lower Triangular Deterministic Model; 3.4.1 Approximate Sum-Capacity; 3.5 Discussion; References; 4 The Information-Theoretic Constant-Gap Optimality of Treating Interference as Noise in Interference Networks; 4.1 Introduction; 4.2 Optimality of Treating Interference as Noise
4.2.1 GDOF Perspective4.2.2 Finite SNR Regime; 4.3 Approximate Optimality; 4.3.1 System Model; 4.3.2 Simple Interference Management in PIMAC; 4.3.3 Upper Bound for the Capacity of the PIMAC; 4.3.4 GDoF Optimality of Simple Schemes; 4.4 Constant Gap Analysis; 4.5 TIN Is Always Sub-optimal; 4.6 Summary; References; 5 Interference-Aware Analog Computation over the Wireless Channel: Fundamentals and Strategies; 5.1 Introduction; 5.1.1 Related Work; 5.1.2 Notation; 5.2 Communication Versus Computation; 5.2.1 The Wireless Multiple-Access Channel; 5.2.2 The Communication Problem