Glossary

8.1 Communication channels and their models

2 min read•july 25, 2024

Communication channels are the backbone of information transfer. They come in two flavors: discrete for digital signals and continuous for analog. Each type has unique characteristics that affect how data moves from sender to .

systems have key components like transmitters and receivers. They also face challenges like , which can mess up signals. Understanding these elements helps us design better ways to send information reliably and efficiently.

Communication Channel Fundamentals

Discrete vs continuous channels

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  • Discrete channels transmit digital or quantized signals handling finite set of possible input and output symbols (digital networks, computer networks)
  • Continuous channels transmit analog signals handling infinite set of possible input and output values (radio broadcasts, telephone lines)
  • Key differences include signal type (digital vs analog), (typically lower for discrete, higher for continuous), and noise susceptibility (discrete channels generally more resistant)

Components of communication systems

  • Information source generates message for transmission
  • encodes message into suitable signal using (amplitude, frequency, )
  • Channel serves as medium for signal travel (wired or wireless)
  • Noise source introduces unwanted disturbances to signal
  • Receiver decodes received signal back into message through demodulation and error correction
  • Destination receives intended message
  • Feedback mechanism allows error detection and correction

Channel Characteristics and Analysis

Channel noise and transmission

  • Noise types include thermal noise (random electron motion in conductors), shot noise (discrete nature of electric charge in electronic devices), and quantization noise (rounding errors in analog-to-digital conversion)
  • Noise effects include reduction, increased , and reduced
  • Mitigation techniques involve , , and and

Probability in channel analysis

  • for discrete channels represents transition probabilities between input and output symbols (P(Y∣X)P(Y|X) where X is input and Y is output)
  • for continuous channels describe likelihood of output values given input values (fY∣X(y∣x)f_{Y|X}(y|x) for continuous random variables X and Y)
  • measures information shared between input and output (I(X;Y)=H(X)−H(X∣Y)I(X;Y) = H(X) - H(X|Y))
  • Channel capacity determines maximum rate of reliable information transmission (: C=max⁡p(x)I(X;Y)C = \max_{p(x)} I(X;Y))
  • and quantify uncertainty in channel input and output (H(X)=−∑p(x)log⁡p(x)H(X) = -\sum p(x) \log p(x) for discrete case, H(X∣Y)=−∑p(x,y)log⁡p(x∣y)H(X|Y) = -\sum p(x,y) \log p(x|y) for conditional entropy)

Key Terms to Review (23)

Amplitude Modulation: Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. It works by varying the strength (amplitude) of the carrier wave in relation to the information signal, which allows audio, video, or other data to be transmitted over communication channels. This method is significant as it makes efficient use of bandwidth and enables the transmission of signals over long distances.
Bandwidth: Bandwidth refers to the maximum data transfer rate of a communication channel, measured in bits per second (bps). It is a crucial aspect of information transmission as it determines how much data can be sent over a channel within a given timeframe, influencing the overall performance and efficiency of communication systems. The concept of bandwidth is essential in understanding both the capacity of different types of channels and the limitations imposed by noise, particularly in Gaussian channels.
Bit error rate: Bit error rate (BER) is a measure of the number of bit errors divided by the total number of transferred bits during a specified time interval. It is a key metric in evaluating the performance and reliability of communication systems, helping to understand how well a system can transmit data accurately over various channels. A lower BER indicates better quality communication, which can be influenced by factors such as noise, interference, and the type of coding used.
Channel: In communication theory, a channel is the medium through which information is transmitted from a sender to a receiver. Channels can be physical, such as wires or airwaves, or abstract, like social networks or protocols. Understanding the properties of channels is essential for analyzing how information flows, the potential for noise or interference, and the overall efficiency of communication systems.
Channel Capacity: Channel capacity is the maximum rate at which information can be reliably transmitted over a communication channel without errors, given the channel's characteristics and noise levels. Understanding channel capacity is essential for optimizing data transmission, developing efficient coding schemes, and ensuring reliable communication in various technologies.
Channel Matrix: A channel matrix is a mathematical representation used to describe the behavior of communication channels, specifically how input signals are transformed into output signals. This matrix provides a way to quantify the probabilities of different outputs given certain inputs, which is essential for understanding the efficiency and reliability of data transmission in communication systems.
Conditional Entropy: Conditional entropy measures the amount of uncertainty remaining about a random variable given the knowledge of another random variable. It quantifies how much additional information is needed to describe one random variable when another is known, and helps in understanding relationships between variables in various contexts, such as communication and data analysis.
Discrete channel: A discrete channel is a type of communication channel that transmits information in discrete, separate symbols rather than in a continuous manner. This means that the data is encoded using a finite set of symbols, allowing for a clear and precise transmission of messages. In the context of communication models, discrete channels are essential for understanding how information is sent, received, and potentially distorted during the transmission process.
Entropy: Entropy is a measure of uncertainty or randomness in a set of data, reflecting the amount of information that is missing when predicting the value of a random variable. In various contexts, entropy quantifies the average amount of information produced by a stochastic source of data, thus providing insights into the efficiency of coding schemes and the capacity of communication systems.
Equalization: Equalization is a signal processing technique used in communication systems to counteract the effects of distortion and interference introduced by a communication channel. It aims to restore the original signal quality by adjusting the received signal to compensate for any amplitude or phase distortions that may occur during transmission. This technique is crucial in ensuring that the received data maintains its integrity and can be accurately interpreted.
Error Correction Codes: Error correction codes are techniques used to detect and correct errors that occur during data transmission or storage. These codes enable a system to recover the original data even when some of it is corrupted, ensuring reliable communication over noisy channels. They play a crucial role in maintaining data integrity by allowing the receiver to identify and fix errors that may arise due to interference or signal degradation.
Filtering: Filtering refers to the process of modifying or selecting signals in a communication channel to enhance the quality of the received information or to remove unwanted components. It plays a crucial role in managing noise and interference in data transmission, ensuring that the intended signal is transmitted and received clearly. This technique is vital for optimizing the performance of communication systems, making it easier to decode the original message accurately.
Frequency Modulation: Frequency modulation (FM) is a method of encoding information in a carrier wave by varying its frequency. This technique is commonly used in communication channels to transmit audio and data signals, allowing for better noise immunity and signal clarity compared to amplitude modulation. FM plays a crucial role in various applications, such as radio broadcasting and telecommunications, providing a reliable means of communication over varying distances.
Modulation techniques: Modulation techniques are methods used to encode information onto a carrier signal for transmission over communication channels. By varying certain properties of the carrier wave, such as its amplitude, frequency, or phase, these techniques allow for effective communication of data across different mediums. These methods are essential in modern technology, enabling various applications such as radio broadcasting, satellite communications, and digital data transmission.
Mutual Information: Mutual information is a measure of the amount of information that one random variable contains about another random variable. It quantifies the reduction in uncertainty about one variable given knowledge of the other, connecting closely to concepts like joint and conditional entropy as well as the fundamental principles of information theory.
Noise: Noise refers to any unwanted or irrelevant signals that interfere with the transmission and reception of information in a communication system. It can distort, degrade, or obscure the original signal, making it difficult for the intended message to be accurately received. Understanding noise is crucial for designing effective communication channels and models that can minimize its impact on information transfer.
Phase Modulation: Phase modulation is a technique used in electronic communication systems where the phase of a carrier signal is varied in accordance with the amplitude of the input signal. This method enables the transmission of information by altering the phase of the waveform, which makes it resilient to noise and interference. Phase modulation plays a critical role in digital communication systems, enabling efficient use of bandwidth and improved data transmission rates.
Probability Density Functions: A probability density function (PDF) is a statistical function that describes the likelihood of a continuous random variable taking on a particular value. It is a fundamental concept in statistics and probability theory, allowing the representation of probabilities over a range of values, rather than at discrete points. The area under the curve of a PDF represents the total probability of the variable falling within a specific interval, which is crucial for analyzing continuous data in various models, including those used in communication channels.
Receiver: In communication theory, a receiver is the entity that receives and interprets the message transmitted over a communication channel. The receiver plays a crucial role in the communication process, as their understanding and interpretation of the message directly impact the effectiveness of the communication. Factors such as noise, encoding, and decoding processes can influence how accurately the receiver understands the transmitted information.
Shannon's Theorem: Shannon's Theorem, also known as the Channel Capacity Theorem, defines the maximum rate at which information can be transmitted over a communication channel without error. This fundamental principle not only laid the groundwork for modern digital communication but also influences various fields like cryptography and data security, revealing the limits and capabilities of communication systems.
Signal-to-noise ratio: Signal-to-noise ratio (SNR) is a measure that compares the level of a desired signal to the level of background noise. A higher SNR indicates a clearer, more distinguishable signal, which is crucial in various applications such as communication systems, where effective transmission of information relies on minimizing noise interference. Understanding SNR helps in evaluating the performance of communication channels and optimizing them for better capacity and efficiency.
Spread spectrum techniques: Spread spectrum techniques are methods used in communication systems that spread a signal over a wider bandwidth than the minimum required to transmit it. This approach provides benefits like resistance to interference, improved security, and the ability to share frequencies with multiple users without causing significant interference. These techniques are essential for enhancing communication performance in various environments, especially where reliable transmission is critical.
Transmitter: A transmitter is a device that converts information into a signal for transmission over a communication channel. It plays a crucial role in the process of communication by modulating data, which allows it to be sent over various mediums, such as air, cables, or optical fibers. Transmitters can vary in complexity from simple radio transmitters to sophisticated digital systems, each designed to ensure accurate and efficient information delivery.
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