## Codes, Graphs, and Systems: A Celebration of the Life and Career of G. David Forney, Jr. on the Occasion of His Sixtieth BirthdayForeword by James L. Massey. Codes, Graphs, and Systems is an excellent reference for both academic researchers and professional engineers working in the fields of communications and signal processing. A collection of contributions from world-renowned experts in coding theory, information theory, and signal processing, the book provides a broad perspective on contemporary research in these areas. Survey articles are also included. Specific topics covered include convolutional codes and turbo codes; detection and equalization; modems; physics and information theory; lattices and geometry; and behaviors and codes on graphs. Codes, Graphs, and Systems is a tribute to the leadership and profound influence of G. David Forney, Jr. The 35 contributors to the volume have assembled their work in his honor. |

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### Contents

THE MUTATIONS OF CONVOLUTIONAL CODING AROUND THE TRELLIS | 3 |

HEAVY TAILS PHASE TRANSITIONS AND THE NATURE OF CUTOFF | 9 |

CONCATENATED CODES WITH CONVOLUTIONAL INNER CODES | 47 |

SOME THOUGHTS ON THE EQUIVALENCE OF SYSTEMATIC AND NONSYSTEMATIC CONVOLUTIONAL ENCODERS | 57 |

SYSTEMATIC BITS ARE BETTER AND NO BUTS ABOUT IT | 77 |

SEQUENCE DETECTION BACKWARD AND FORWARD IN TIME | 93 |

LEAST SQUARES AND KALMAN FILTERING ON FORNEY GRAPHS | 113 |

ITERATIVE ALGORITHMS FOR MAXIMUM LIKELIHOOD SEQUENCE DETECTION | 137 |

POWER LIMITED CHANNELS CODING MULTIACCESS AND SPREAD SPECTRUM | 229 |

RECURSIVE CONSTRUCTION OF MULTICHANNEL TRANSMISSION LINES WITH A MAXIMUM ENTROPY PROPERTY | 259 |

ON THE CAPACITY OF MULTIMODE OPTICAL FIBERS | 291 |

HUFFMAN SHAPING | 299 |

LATTICES AND CRYPTOGRAPHY | 317 |

A SIMPLE CONSTRUCTION FOR THE BARNESWALL LATTICES | 333 |

MINIMAL BASES OF RATIONAL VECTOR SPACES AND THEIR IMPORTANCE IN ALGEBRAIC SYSTEMS THEORY | 345 |

FINITE GEOMETRY LOW DENSITY PARITYCHECK CODES CONSTRUCTION STRUCTURE AND DECODING | 359 |

V92 THE FINAL CHAPTER IN THE NEVERENDING STORY OF DIALUP MODEMS | 159 |

MODEMS TO MARS | 179 |

EXISTENCE OF GOOD CODES WITH LOW PEAKTOAVERAGE POWER RATIOS FOR MULTICARRIER COMMUNICATIONS | 187 |

ON SYNCHRONIZATION AND INTERSYMBOL INTERFERENCE FOR JAMMED TIMING CHANNELS | 201 |

DECODING ONLY THE STRONGEST CDMA USERS | 217 |

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achieve assume binary bit error block codes capacity channel code bit codeword columns Communications complexity computational constellation constituent encoders constraint convolutional codes corresponding David Forney decoding algorithms defined denote density distribution EG-LDPC code EG(m Equation error performance error probability example factor graphs finite geometry finite geometry LDPC follows Forney graph function G. D. Forney geometry LDPC code given Hamming code IDBP IEEE Transactions Information Theory input integer intersymbol interference iterative decoding jammer lattice Lemma linear linear code lower bound matrix H mergeable minimal minimum distance modem nodes nonsystematic NP-complete OFDM optimal output packet parity-check matrix points polynomial problem random rows Schur self-dual code sequence detection sequential decoding Shannon limit shaping gain shown in Figure signal solution symbol systematic Tanner graph Theorem tion Transactions on Information transmitted trellis formation turbo codes users variables vertex vertices weight zero

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Page iv - INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE COMMUNICATIONS AND INFORMATION THEORY Other books in the series: Consulting Editor Robert Gallager CODES,