6.13: Digital Communication

Learning Objectives

• A very brief introduction to digital communication and its importance in error-free transmission of information.

Effective, error-free transmission of a sequence of bits—a bit stream $$\{ b(0), b(1), ...\}$$ —is the goal here. We found that analog schemes, as represented by amplitude modulation, always yield a received signal containing noise as well as the message signal when the channel adds noise. Digital communication schemes are very different. Once we decide how to represent bits by analog signals that can be transmitted over wireline (like a computer network) or wireless (like digital cellular telephone) channels, we will then develop a way of tacking on communication bits to the message bits that will reduce channel-induced errors greatly. In theory, digital communication errors can be zero, even though the channel adds noise!

We represent a bit by associating one of two specific analog signals with the bit's value. Thus, if $$b(n) = 0$$, we transmit the signal $$s_0(t)$$; if $$b(n) = 1$$, send $$s_1(t)$$. These two signals comprise the signal set for digital communication and are designed with the channel and bit stream in mind. In virtually every case, these signals have a finite duration $$T$$ common to both signals; this duration is known as the bit interval. Exactly what signals we use ultimately affects how well the bits can be received. Interestingly, baseband and modulated signal sets can yield the same performance. Other considerations determine how signal set choice affects digital communication performance.

Exercise $$\PageIndex{1}$$

What is the expression for the signal arising from a digital transmitter sending the bit stream $$b(n), n=\{...,-1,0,1,...\}$$ using the signal set $$s_0(t)$$, $$s_1(t)$$, each signal of which has duration $$T$$?

Solution

$x(t)=\sum_{n=-\infty }^{\infty }s_{b_{n}}(t-nT)$

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