Test Your Understanding of the Nyquist Limit and Binary Amplitude Encoding

The main focus of the Physical layer in computer networks is the transfer of information through various mediums such as electrical signals, optical signals, and EM waves.

Examples of information carriers include sound waves, quantum states, proteins, ink & paper, etc.

Topics covered in the Datalink layer include introduction, framing, error coding, and switched networks.

The purpose of error coding is to detect and correct errors that occur during data transmission in order to ensure reliable communication.

Examples of protocols in the Application Layer include ftp and http.

Channel capacity is the maximum data rate that can be transmitted through a communication channel without errors.

Baseband modulation sends the 'bare' signal, while carrier modulation uses the signal to modulate a higher frequency signal (carrier).

The three ways to modulate a sinusoidal wave are amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM).

The purpose of amplitude modulation (AM) is to change the strength of the signal.

The purpose of frequency modulation (FM) is to change the frequency of the signal.

The purpose of phase modulation (PM) is to change the phase of the signal.

The Nyquist limit states that a noiseless channel of width H can at most transmit a binary signal at a rate 2 x H.

The Nyquist Limit states that a noiseless channel of width H can at most transmit a binary signal at a rate of 2 x H.

To overcome the Nyquist Limit, instead of using binary encoding, we can use lots of different values for transmission.

The channel bandwidth is determined by the transmission medium and the quality of the transmitter and receivers.

Shannon's theorem states that the maximum capacity (C) of a noisy channel is equal to the channel bandwidth (B) multiplied by the logarithm base 2 of (1 + S/N), where S/N is the signal to noise ratio of the channel.

Noise, attenuation, and dispersion are the limitations that affect the data rate a channel can sustain.

Multiple channels can coexist by transmitting at different frequencies, at different times, or in different parts of space.

FDM allows different users to use different parts of the frequency spectrum.

TDM allows different users to send at different times.

FDM and TDM can be combined to allow users to send at reduced rate all the time or at full speed some of the time.

Twisted pair copper wire provides noise immunity and can be combined with Differential Signaling.

Typical limit of multimode fiber is 1 Gbps at 100m.

Typical limit of single mode fiber is 10 Gbps at 60 km or more.

multipath fading, security

MAC and other rules, aggressive encoding techniques

physical properties of media

limited by physical properties of media

C = B x log2(1 + S/N)

space, time, or frequency division multiplexing

Baseband modulation involves sending the 'bare' signal, while carrier modulation involves using the signal to modulate a higher frequency signal (carrier).

The Nyquist limit states that a noiseless channel of width H can at most transmit a binary signal at a rate 2 x H.

The purpose of amplitude modulation is to change the strength of the signal.

The purpose of frequency modulation is to change the frequency of the signal.

The purpose of phase modulation is to change the phase of the signal.

Transmitter/receiver complexity, power requirements, bandwidth, medium (air, copper, fiber, etc.), noise immunity, range, and multiplexing.

C = B \cdot \log_2(1 + \frac{S},{N})

10 \cdot \log(S/N)

3200 \cdot \log_2(1 + 1000) = 31.895 \text{ kbits/s}

Throughput = 2 \cdot \text{Channel Bandwidth}

Frequency, space, time

To determine which user gets to send when

Electrical signals (on a wire) and Optical signals (in a fiber).

EM waves, Sound waves, Quantum states, Proteins, Ink & paper, etc.

To vary the amplitude of a carrier wave in proportion to the waveform being transmitted.

To vary the phase of a carrier wave in proportion to the waveform being transmitted.

To vary the frequency of a carrier wave in proportion to the waveform being transmitted.

Shannon's theorem states that the capacity of a noisy channel can be calculated using the formula: $C = B\log_2(1 + \frac{S}{N})$, where C is the capacity, B is the bandwidth, S is the signal power, and N is the noise power.

Aggressive encoding techniques can include error correction coding, channel coding, and modulation schemes that can improve the signal-to-noise ratio.

The equation is $C = B \cdot \log_2(1 + \frac{S}{N})$, where C is the channel capacity, B is the bandwidth, S is the signal power, and N is the noise power.

Multiple users can be supported using space division multiplexing, time division multiplexing, or frequency division multiplexing techniques.

Different transmission media include copper, optical, and wireless. Each media has its own characteristics such as bandwidth, distance limitations, susceptibility to interference, and attenuation.

Some effects that can impact wireless network performance include multipath fading, interference, and security issues.

The Nyquist formula is a rough idea of idealized throughput and is given by $2B \log_2(V)$, where B is the bandwidth and V is the number of different voltage levels that can be transmitted.

Advantages: high bandwidth, low attenuation, immune to electromagnetic interference, long distance transmission. Disadvantages: higher cost, more fragile, requires specialized equipment.

Modulation is used to encode information onto a carrier signal, allowing it to be transmitted over a medium.

Multimode fiber has a larger core that allows multiple modes of light to propagate, while single mode fiber has a smaller core that allows only a single mode of light to propagate. Single mode fiber has higher bandwidth and longer transmission distances compared to multimode fiber.

Wavelength division multiplexing allows multiple wavelengths of light to be transmitted simultaneously over a single fiber, increasing the capacity of the fiber.

Wireless technologies have high attenuation, limited range, and are susceptible to interference from other transmitters.

The distance limit of fiber optic transmission can be extended through regeneration or amplification. Regeneration involves electronically regenerating the signal, while amplification uses erbium doped fiber amplifiers to boost the signal strength.

C = B \cdot \log_2(1 + \frac{S},{N})

C = 3200 \cdot \log_2(1 + \frac{1000},{1}) = 31.895 \text{ kbits/s}

Noise, attenuation, and dispersion

To support multiple channels by allowing different users to transmit at different frequencies, times, or parts of space

Frequency, space, and time

To control which user gets to send data when

Sound waves, Quantum states, Proteins, Ink & paper, etc.

Wireless technologies, Channel bandwidth, Noise, Interference, etc.

Bandwidth, Noise immunity, Power efficiency, Complexity, etc.

To coordinate access to the shared channel and prevent collisions.

Generally, as the distance increases, the available bandwidth decreases.

The maximum amount of information that can be transmitted through a channel per unit of time.

C = B \ imes log_2(1 + \ rac{S}{N})

To make the signal less sensitive to noise

C = B \ imes log_2(1 + \ rac{S}{N})

Multipath fading, security, limited bandwidth

To control the use of the limited bandwidth

Transmission medium and transmit/receive hardware

Baseband modulation has the advantage of simpler hardware and the ability to control the range of frequencies used. However, it may cause problems due to the highest frequencies being many times higher than low frequencies.

Bandwidth is the width of the frequency range in which the Fourier transform of the signal is nonzero.

The Nyquist limit states that a noiseless channel of width H can at most transmit a binary signal at a rate 2 x H.

The purpose of carrier modulation is to use the signal to modulate a higher frequency signal (carrier), which can be viewed as the product of the two signals.

Transmitter/receiver complexity, power requirements, bandwidth, medium (air, copper, fiber, ...), noise immunity, range, and multiplexing are all factors that determine the choice of modulation method.

Some properties of different transmission media include cost, bandwidth capacity, distance limitations, and resistance to interference.

Erbium doped fiber amplifiers offer up to 40 dB gain and linear response over a broad spectrum, making amplification over long distances practical.

Signal strength attenuates quickly as distance increases, following the inverse cube law (1/d^3).

Wavelength division multiplexing allows for the transmission of multiple wavelengths through the same fiber, enabling each wavelength to carry a separate signal.

Typically, multimode fiber has a limit of 1 Gbps at 100m.

Typically, single mode fiber has a limit of 10 Gbps at 60 km or more.

The distance limit of fiber optic transmission can be extended through the use of regeneration or amplification at the end of the span. Erbium doped fiber amplifiers are often used for amplification.

The three ways to modulate a sinusoidal wave are amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM).

Some factors that determine network properties are transmitter/receiver complexity, power requirements, bandwidth, medium (air, copper, fiber), noise immunity, range, and multiplexing.

Bandwidth is the width of the frequency range in which the Fourier transform of the signal is nonzero. It is the range of frequencies in which there is energy.

A (periodic) signal can be viewed as a sum of sine waves of different strengths in the frequency domain. It corresponds to energy at different frequencies.

The Nyquist limit states that a noiseless channel of width H can transmit a binary signal at a maximum rate of 2 x H.

The purpose of multiplexing in data transmission is to allow multiple signals to share a single transmission medium by dividing the bandwidth into multiple channels.

The Nyquist limit states that a noiseless channel of width H can at most transmit a binary signal at a rate of 2 x H.

Shannon's theorem, C = B x log2(1 + S/N), is used to calculate the maximum capacity (C) of a noisy channel. C represents the maximum data rate in bits per second, B represents the channel bandwidth in Hz, and S/N represents the signal-to-noise ratio of the channel.

Some factors that can impact network performance include noise, attenuation, and dispersion. These can limit the data rate that a channel can sustain and affect different technologies in different ways.

Multiple channels can be supported through frequency multiplexing, where different users use different parts of the spectrum, or through time division multiplexing, where different users use the wire at different points in time. Media access control (MAC) is also used to control the access to the channel.

Some limitations to the data rate that a channel can sustain include noise, attenuation, and dispersion. These effects become worse with distance and can vary depending on the technology used.

Different transmission media have different properties such as bandwidth, attenuation, and noise susceptibility. For example, copper wires have limited bandwidth and are susceptible to noise, while fiber optic cables have high bandwidth and are less susceptible to noise.

A fiber optic cable consists of a core surrounded by cladding, with the core having a lower index of refraction than the cladding. This structure allows for the propagation of light through the core by reflecting it off the cladding, minimizing signal loss. The minimum bend radius of the cable is a few centimeters.

Multimode fiber has a larger core diameter (62.5 or 50 microns) and can carry multiple modes of light. It is typically used with LED sources and is subject to mode dispersion, where different modes travel at different speeds. Single mode fiber, on the other hand, has a smaller core diameter (8 microns) and can carry only a single mode of light. It is usually used with laser diode sources and is still subject to chromatic dispersion.

Copper twisted pair cables (UTP) have a maximum distance of 100 meters and can support data rates of up to 1 Gbps for Category 5 cables. Coax cables can support gigabit speeds up to a kilometer. Multimode fiber can support data rates of up to 1 Gbps at 100 meters, while single mode fiber can support data rates of up to 10 Gbps at distances of 60 kilometers or more.

The distance limit of fiber optic transmission can be extended through regeneration or amplification. Electronic repeaters can be used to regenerate the signal, but they may introduce delay. Amplification can be achieved using erbium doped fiber amplifiers, which offer up to 40 dB gain and linear response over a broad spectrum. This allows for high-speed transmission over long distances, such as 40 Gbps at 500 kilometers.

Wavelength division multiplexing (WDM) is a technique used to send multiple wavelengths of light through the same fiber. The optical signal is multiplexed and demultiplexed on the fiber, with each wavelength representing an optical carrier that can carry a separate signal. This allows for high-speed transmission of multiple signals over a single fiber. For example, WDM can support 16 colors of 2.4 Gbps each.

Wireless technologies offer convenience and mobility, but they have limitations in terms of distance and signal strength. Signals propagate out as spheres, and the signal strength attenuates quickly with distance, following the inverse square law (1/d^3). Additionally, wireless technologies suffer from high noise due to interference from other transmitters, which further limits their range.

Aggressive encoding techniques can include error correction codes, such as Reed-Solomon codes, and modulation schemes that are more robust against noise, such as QAM.

The equation for calculating the channel capacity according to Shannon's theorem is $C = B \log_2(1 + \frac{S}{N})$.

The Nyquist formula for idealized throughput is $T = 2B \log_2 V$, where T is the throughput, B is the bandwidth, and V is the number of levels that can be distinguished.

Different transmission media have different properties such as bandwidth, attenuation, noise susceptibility, and dispersion. For example, copper cables have limited bandwidth and are susceptible to noise, while optical fibers have high bandwidth and are less susceptible to noise.

Multiple users can be supported in a network through techniques such as space division multiplexing, time division multiplexing, and frequency division multiplexing. These techniques allocate different resources, such as physical space, time slots, or frequency bands, to different users to enable simultaneous communication.

The relationship between bandwidth and distance in networks is that the available bandwidth and achievable data rate decrease with increasing distance. This is due to physical properties of the transmission medium, such as attenuation and dispersion.

The different types of information carriers include electrical signals (on a wire), optical signals (in a fiber), EM waves, sound waves, quantum states, proteins, ink & paper, etc.

Some examples of modulation techniques used in data transmission include amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM).

The main topics covered in the Physical Layer lecture include modulation and coding techniques, channel capacity, framing, error coding, switched networks, broadcast-networks, and home networking.

The purpose of media access control (MAC) in supporting multiple channels is to coordinate and manage the access of multiple devices to the shared network medium.

The formula for calculating the maximum capacity (C) of a noisy channel using Shannon's theorem is $C = B \cdot \log_2(1 + \frac{S}{N})$, where C is the channel capacity, B is the bandwidth, S is the signal power, and N is the noise power.

Some examples of transmission media include wires (for electrical signals), fibers (for optical signals), and wireless channels (for EM waves).