# Network Information Theory # Network Information Theory

Language: English

Pages: 714

ISBN: 1107008735

Format: PDF / Kindle (mobi) / ePub

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Bounds on the Optimal Rate Region 259 10.3 Slepian–Wolf Theorem 260 10.4 Lossless Source Coding with a Helper 264 10.5 Extensions to More than Two Sources Summary 269 270 Bibliographic Notes 270 Problems 271 11 Lossy Compression with Side Information 274 11.1 Simple Special Cases 275 11.2 Causal Side Information Available at the Decoder 275 11.3 Noncausal Side Information Available at the Decoder 11.4 Source Coding When Side Information May Be Absent Summary 280 286 288

, n) codes with average power P and limn→∞ Pe(n) = 0, we must have R≤ 1 log(1 + д 2 P). 2 Substituting P = ER, we obtain the lower bound on the energy per bit E ≥ (22R − 1)/(д 2 R). 52 Point-to-Point Information Theory We also know that if the average power of the code is P, then any rate R < C(д 2 P) is achievable. Therefore, reliable communication at rate R with energy per bit E > (22R − 1)/R is possible. Hence, the energy-per-bit–rate function, that is, the minimum energyper-bit needed

coding, successive refinement of information, and network coding, are being implemented in real-world networks. xviii Preface Development of the Book The idea of writing this book started a long time ago when Tom Cover and the first author considered writing a monograph based on their aforementioned  survey paper. The first author then put together a set of handwritten lecture notes and used them to teach a course on multiple user information theory at Stanford University from  to

< H(Y1 |U1 , Q) + H(Y2 |U2 , Q) − H(T1 |U1 , Q) − H(T2 |U2 , Q), 2R1 + R2 < H(Y1 |Q) + H(Y1 |U1 , U2 , Q) + H(Y2 |U2 , Q) − H(T1 |U1 , Q) − 2H(T2 |U2 , Q), 150 Interference Channels R1 + 2R2 < H(Y2 |Q) + H(Y2 |U1 , U2 , Q) + H(Y1 |U1 , Q) − 2H(T1 |U1 , Q) − H(T2 |U2 , Q) for some pmf p(q)p(x1 |q)p(x2 |q)pT1 |X1 (u1 |x1 )pT2 |X2 (u2 |x2 ). Considering the Gaussian IC, we obtain a corresponding inner bound with differential entropies in place of entropies. This inner bound coincides with the

(.) for some pmf p(x1 )p(x2 ). A similar linear coding technique can be readily developed for any q-ary alphabet, dimension L, and α ∈ [0, 2] that achieves the entire capacity region by treating interference as noise. 6.8.1* QED-IC Approximation of the Gaussian IC Considering the normalized capacity region characterization in (.) and (.), we can show that the normalized symmetric capacity of the symmetric QED-IC is ???? Csym = min????1, max{α/2, 1 − α/2}, max{α, 1 − α}???? (.) ∗ for α ∈