## Lattice Coding for Signals and Networks: A Structured Coding Approach to Quantization, Modulation, and Multiuser Information TheoryUnifying information theory and digital communication through the language of lattice codes, this book provides a detailed overview for students, researchers and industry practitioners. It covers classical work by leading researchers in the field of lattice codes and complementary work on dithered quantization and infinite constellations, and then introduces the more recent results on 'algebraic binning' for side-information problems, and linear/lattice codes for networks. It shows how high dimensional lattice codes can close the gap to the optimal information theoretic solution, including the characterisation of error exponents. The solutions presented are based on lattice codes, and are therefore close to practical implementations, with many advanced setups and techniques, such as shaping, entropy-coding, side-information and multi-terminal systems. Moreover, some of the network setups shown demonstrate how lattice codes are potentially more efficient than traditional random-coding solutions, for instance when generalising the framework to Gaussian networks. |

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### Contents

Summary | 34 |

Summary | 56 |

1 | 84 |

Infinite constellation for modulation | 110 |

Asymptotic goodness | 134 |

Nested lattices | 178 |

Lattice shaping | 197 |

Sideinformation problems | 247 |

Modulolattice modulation | 295 |

Gaussian networks | 313 |

4 | 341 |

Error exponents | 372 |

Appendix | 400 |

408 | |

425 | |

### Other editions - View all

Lattice Coding for Signals and Networks: A Structured Coding Approach to ... Ram Zamir Limited preview - 2014 |

### Common terms and phrases

achieves additive-noise channel asymptotically AWGN channel ball binary binning CAWGN channel capacity channel coding coarse lattice codebook codeword coding rate coding scheme conditional entropy coset Definition denote density differential entropy dimension distortion measure distribution dither dithered quantization ECDQ encoder entropy equivalent error exponent error probability Euclidean Figure follows fundamental cell gap to capacity Gaussian high SNR high-dimensional information theory integer interference lattice codes lattice constellation lattice decoding lattice point lattice quantizer Lemma linear code lower bound matrix MHS ensemble ML decoding mod channel modulo operation modulo-uniform multiple-access mutual information n-dimensional nested lattices noise-matched NVNR ofthe optimal output packing partition problem proof radius random coding rate-distortion function scalar Section sequence Shannon Shannon capacity shaping side information source coding sphere Theorem transmitted uniform upper bounded variance vector volume Voronoi cell Voronoi modulation white-Gaussian Wyner–Ziv zero