By John R. Pierce

ISBN-10: 0486134970

ISBN-13: 9780486134970

Covers encoding and binary digits, entropy, language and which means, effective encoding and the noisy channel, and explores ways that details idea pertains to physics, cybernetics, psychology, and paintings. "Uncommonly good...the such a lot pleasing dialogue to be found." - medical American. 1980 variation.

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**Example text**

5) which corresponds to a strategy where the source transmits the signal isotropically (that is, its probability density function is invariant to multiplication by a unitary matrix). 2 The Outage Probability The outage probability is a key concept in wireless communications. 5) becomes a random variable which is denoted by C(H). 1): Ynr ×T = Hnr ×nt Xnt ×T + Znr ×T . Whenever the data rate R is lower than C(H), then it is possible to ﬁnd a code which achieves an arbitrarily low error probability.

Finally, we require the codes to have a non-vanishing determinant. In the next chapter, we will look at the code design from an information theoretic point of view. This page intentionally left blank 3 An Information Theoretic Perspective In this chapter, we will see that two main features are important, to ensure the good performance of a coding scheme from an information theoretic point of view: (i) reaching the diversity-multiplexing gain trade-oﬀ and (ii) using information lossless codes. We will see that both these properties will correspond to other properties already required.

Nr . 12) to the expression of the outage probability at high SNR, we get n SIMO Pout (R) 2R − 1 r ≈ . 13) Now, the outage probability asymptotically decays as 1/SNRnr , hence nr is the diversity order of this channel. d. zero-mean Gaussian. 14) . 16) enlightening a transmit diversity order equal to nt . 4 The MIMO Case The calculation of the outage probability for the MIMO case is more diﬃcult than for the previous above cases, but we can start by intuitively explaining the behavior of the SNR exponent.

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