DATA RATE LIMITS Lecture 5
Data Rate • A very important consideration in data communications is how fast we can send data, in bits per second over a channel. Data rate depends on three factors: 1. The bandwidth available 2. The level of the signals we use 3. The quality of the channel (the level of noise) • Two theoretical formulas were developed to calculate the data rate: 1. Nyquist for a noiseless channel. 2. Shannon for a noisy channel.
Noiseless Channel: Nyquist Bit Rate • For a noiseless channel, the Nyquist bit rate formula defines the theoretical maximum bit rate • 𝐵𝑖𝑡𝑅?𝑡? = 2 ? ?????𝑖?𝑡ℎ ? 𝑙?𝑔 2 𝐿 • Where, bandwidth is the bandwidth of the channel, L is the number of signal levels used to represent data. and BitRate is the bit rate in bits per second.
Noiseless Channel: Nyquist Bit Rate • According to the formula, we might think that, given a specific bandwidth, we can have any bit rate we want by increasing the number of signal levels. Although the idea is theoretically correct, practically there is a limit. • When increase the number of signal levels, we impose a burden on the receiver. If the number of levels in a signal is just 2, the receiver can easily distinguish between a 0 and a 1. • If the level of a signal is 64, the receiver must be very sophisticated to distinguish between 64 different levels. • So, increasing the levels of a signal reduces the reliability of the system.
Noisy Channel: Shannon Capacity • In reality, we cannot have a noiseless channel; the channel is always noisy. In 1944, Claude Shannon introduced a formula, called the Shannon capacity, to
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