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Unformatted text preview: ECE 5670 : Digital Communications Lecture 4: Energy Efficient Communication 1 2/8/2011 Instructor: Salman Avestimehr Introduction So far, we have seen that block communication (using the simple repetition coding) can improve the reliability of communication, significantly over and above that possible with sequential communication. This is particularly true when we want to communicate a large amount of data. But this has come at a high cost: specifically we can get arbitrarily reliable communication, but the data rate (number of bits per unit time sample) goes to zero. Specifically, we know from Lecture 3 that the data rate is B n = log 2 n 2 n o ( n ) , (1) where we used the notation o ( n ) to denote a function of n that has the property that lim n o ( n ) = 0 . (2) Simply put we can think of the data rate of reliable communication with repetition coding as approximately log 2 n 2 n (3) which is very small for large n . For a large data packet (of size, say B ), we need an amount of time approximately 2 2 B to communicate it reliably using repetition coding! it is very energy inefficient. A measure of energy efficiency is the amount of energy (in Joules) consumed per bit that is reliably communicated. In the repetition coding scheme, using n time instants we are using a total energy nE . Further, we need 2 2 B time samples to send B bits reliably. So we use up energy proportional to 2 2 B and thus the energy per bit is 2 2 B E B . (4) For large data size B , this goes to infinity: the repetition coding scheme is hardly energy efficient. In summary, repetition coding significantly improved the reliability of communication over sequential communication, particularly for large data packets, but at the cost of zero data rate and zero energy efficiency. 1 Based on lecture notes of Professor Pramod Viswanath at UIUC. This is in stark contrast to sequential communication that had non-zero data rate and energy efficiency: after all, we keep transmitting new information bits at every time sample (so the data rate is non-zero) and we only use a finite energy at any time sample (so the energy efficiency is also non-zero). Question : Can we have the desirable features of sequential communication, non-zero data rate and energy efficiency, while ensuring that the reliability is very good? In other words, is there a free breakfast, lunch and dinner? Well, the short answer is yes . The long answer is that the block communication scheme that does it is quite involved. It actually is rocket-science (almost!). We will spend several lectures trying to figure out what it takes to reliably communicate at non-zero data rates and non-zero energy efficiency. It is a remarkable success story that has drawn various aspects of electrical engineering: role of modeling, asking the right questions, mathematical abstraction, mathematical legerdemain, algorithmic advances and, finally, advances in circuits to handle the computational complexity of the algorithms involved.the computational complexity of the algorithms involved....
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- Spring '11