## Coding for Channels with FeedbackCoding for Channels with Feedback presents both algorithms for feedback coding and performance analyses of these algorithms, including analyses of perhaps the most important performance criterion: computational complexity. The algorithms are developed within a single framework, termed the compressed-error-cancellation framework, where data are sent via a sequence of messages: the first message contains the original data; each subsequent message contains a source-coded description of the channel distortions introduced on the message preceding it. Coding for Channels with Feedback provides an easily understood and flexible framework for deriving low-complexity, practical solutions to a wide variety of feedback communication problems. It is shown that the compressed-error-cancellation framework leads to coding schemes with the lowest possible asymptotic order of growth of computations and can be applied to discrete memoryless channels, finite state channels, channels with memory, unknown channels, and multiple-access channels, all with complete noiseless feedback, as well as to channels with partial and noisy feedback. This framework leads to coding strategies that have linear complexity and are capacity achieving, and illustrates the intimate connection between source coding theory and channel coding theory. Coding for Channels with Feedback is an excellent reference for researchers and communication engineers in the field of information theory, and can be used for advanced courses on the topic. |

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### Contents

An Introduction to the Framework | 9 |

B Proof of Subsystem Property 2 | 46 |

References | 60 |

Copyright | |

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### Common terms and phrases

algorithm asymptotic block blocklength capacity region capacity-achieving channel inputs channel output channels with feedback Chapter codebook coding scheme compressed-error-cancellation framework constant corresponding crossover probability CSWCF decays exponentially defined denote developed DFSC DFSCf's DMCf DMCf's encoding and decoding entropy ergodic error exponent error probability expander codes exponentially decaying false alarm feedback channel feedback rate feedback-free capacity follows forward channel function Information Theory inner code input distribution iteration Kullback-Leibler distance Lemma Lempel-Ziv linear linear-complexity Markov process message bits modified scheme mSB coding multiple-access channels mutual information noiseless feedback number of channel On(n outer code parameters partial feedback precoder precoder and source probability of error Proof random variable receiver resulting from passing retransmission samples sends Slepian-Wolf coded feedback Slepian-Wolf coding source coder space complexity stopping rule Subsystem Property superchannel SWCF synchronization sequence termination coding tion transmission transmitter uniform convergence upper bound variable-length code verification sequences