DATA RATE LIMITS
- 1. DATA RATE LIMITS D AT E 2 0 - 1 0 - 2 0 2 0
- 2. DATA RATE LIMITS L E C T U R E 9 D AT E 2 0 - 1 0 - 2 0 2 0
- 3. DATA RATE LIMITS: • 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)
- 4. DATA RATE LIMITS: • Two theoretical formulas were developed to calculate the data rate: 1. Nyquist bit rate for a noiseless channel BitRate = 2 * bandwidth * log 2 L 2: Shannon Capacity for a noisy channel Capacity = bandwidth * log 2 (1 + SNR)
- 5. NOISELESS CHANNEL: NYQUIST BIT RATE • For a noiseless channel, the Nyquist bit rate formula defines the theoretical maximum bit rate BitRate = 2 x bandwidth x 10g2 L • In this formula, 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. • When we increase the number of signal 1eve1s, 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. In other words, increasing the levels of a signal reduces the reliability of the system. • Note: Increasing the levels of a signal may reduce the reliability of the system.
- 6. EXAMPLE 3.34 OF ( NOISELESS CHANNEL: NYQUIST BIT RATE) • Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels. The maximum bit rate can be calculated as Given data: bandwidth b = 3000 Hz level of signal L = 2 bit rate = ? BitRate = 2 x bandwidth x 10g2 L BitRate =2 x 3000 x log2 2 =6000 bps
- 7. 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 determine the theoretical highest data rate for a noisy channel: Capacity =bandwidth X log2 (1 +SNR) • In this formula, bandwidth is the bandwidth of the channel, SNR is the signal-to noise ratio, and capacity is the capacity of the channel in bits per second. Note that in the Shannon formula there is no indication of the signal level, which means that no matter how many levels we have, we cannot achieve a data rate higher than the capacity of the channel. In other words, the formula defines a characteristic of the channel, not the method of transmission.
- 8. EXAMPLE 3.37 ( NOISY CHANNEL: SHANNON CAPACITY) • Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zero. In other words, the noise is so strong that the signal is faint. For this channel the capacity C is calculated as C=B log2 (1 + SNR) C=B 10g2 (l + 0) C=B log2 1 C = B x 0 = 0 • This means that the capacity of this channel is zero regardless of the bandwidth. In other words, we cannot receive any data through this channel.
- 9. PERFORMANCE (NETWORK PERFORMANCE) : • Up to now, we have discussed the tools of transmitting data (signals) over a network and how the data behave. One important issue in networking is the performance of the network-how good is it? We discuss quality of service, an overall measurement of network performance. Bandwidth: One characteristic that measures network performance is bandwidth. However, the term can be used in two different contexts with two different measuring values: bandwidth in hertz and bandwidth in bits per second.
- 10. BANDWIDTH: Bandwidth in Hertz: • Bandwidth in hertz is the range of frequencies contained in a composite signal or the range of frequencies a channel can pass. For example, we can say the bandwidth of a subscriber telephone line is 4 kHz. Bandwidth in Bits per Seconds: • The term bandwidth can also refer to the number of bits per second that a channel, a link, or even a network can
- 11. RELATIONSHIP AND IN NETWORKING, WE USE THE TERM BANDWIDTH IN TWO CONTEXTS: Relationship: • There is an explicit relationship between the bandwidth in hertz and bandwidth in bits per seconds. Basically, an increase in bandwidth in hertz means an increase in bandwidth in bits per second. • In networking, we use the term bandwidth in two contexts. • The first, bandwidth in hertz, refers to the range of frequencies in a composite signal or the range of frequencies that a channel can pass. • The second, bandwidth in bits per second, refers to the speed of bit transmission in a channel or link.
- 12. THROUGHPUT: Throughput: • The throughput is a measure of how fast we can actually send data through a network. • The throughput is an actual measurement of how fast we can send data. For example, we may have a link with a bandwidth of 1 Mbps, but the devices connected to the end of the link may handle only 200 kbps. This means that we cannot send more than 200 kbps through this link.
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