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Semester 2: M.Sc. Electronics and Communication Semester -II
Information Theory: Entropy, Information rate, Coding theorems
Information Theory: Entropy, Information Rate, Coding Theorems
Entropy
Entropy is a measure of uncertainty or randomness in information theory. It quantifies the amount of unpredictability in a set of possible outcomes. The higher the entropy, the more uncertain the outcome, and conversely, a lower entropy indicates more predictability. For a discrete random variable X with possible outcomes x1, x2, ..., xn occurring with probabilities p1, p2, ..., pn, the entropy H(X) is defined as H(X) = -∑(pi * log(pi)), where the logarithm is typically base 2. This concept is crucial for understanding the limits of data compression and transmission.
Information Rate
Information rate, also known as channel capacity, refers to the maximum rate at which information can be reliably transmitted over a communication channel. It is typically measured in bits per second (bps). The Shannon-Hartley theorem establishes a relationship between the information rate, bandwidth of the communication channel, and the noise present in the channel. It states that the maximum information rate C is given by C = B * log2(1 + S/N), where B is the bandwidth in hertz, S is the average signal power, and N is the average noise power.
Coding Theorems
Coding theorems in information theory provide the framework for lossless and lossy data compression. Two fundamental coding theorems are Shannon's source coding theorem and Shannon's channel coding theorem. The source coding theorem states that data can be compressed to its entropy without losing information, while the channel coding theorem states that it is possible to transmit information over a noisy channel at a rate close to the channel capacity with an arbitrarily small probability of error when appropriate coding strategies are applied. These theorems form the basis for modern digital communication and data storage systems.
Hamming weight, Hamming distance, Linear Block codes, Cyclic codes
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The Hamming weight of a binary string is the number of symbols that are different from the zero symbol. It is a measure of how many bits in the string are set to one.
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Hamming distance is defined as the number of positions at which the corresponding symbols are different between two strings of the same length. It is used to measure the error between received and transmitted data.
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Linear block codes are error-correcting codes wherein each codeword can be expressed as a linear combination of a set of basis codewords. They are characterized by parameters such as the length of the codeword, the number of data bits, and the minimum Hamming distance.
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Cyclic codes are a subset of linear block codes with the property that if a codeword is in the code, then any cyclic shift of that codeword is also in the code. This property makes them particularly useful for efficient encoding and decoding.
Convolutional codes, Turbo coding, Cryptography, DES, public key cryptography
Convolutional codes, Turbo coding, Cryptography, DES, Public key cryptography
Convolutional Codes
Convolutional codes are a type of error-correcting code that encode data in a way that allows for the detection and correction of errors that may occur during transmission. They use a memory element to hold a portion of the data, creating a relationship between the input and output sequences. Convolutional codes are often used in communication systems where data integrity is crucial.
Turbo Coding
Turbo coding is a form of error correction that employs two or more convolutional codes and an interleaver to improve error correction capabilities. It was developed to approach the Shannon limit, making it highly efficient in high noise environments. Turbo codes are widely used in applications such as mobile communication and satellite communications.
Cryptography
Cryptography is the practice of securing information by transforming it into an unreadable format for unauthorized users. It employs algorithms and keys to encrypt and decrypt data, ensuring the confidentiality, integrity, and authenticity of information. Cryptographic methods are essential in securing communication and protecting sensitive data.
Data Encryption Standard (DES)
DES is a symmetric-key algorithm for the encryption of digital data. It uses a fixed size key of 56 bits and operates on 64-bit blocks of data. DES was widely used for securing data but has become less secure due to advancements in computational power. It has largely been replaced by more secure algorithms like AES.
Public Key Cryptography
Public key cryptography, also known as asymmetric cryptography, uses a pair of keys - a public key and a private key. The public key is shared openly to encrypt data, while the private key is kept secret for decryption. This method enables secure communication and is fundamental in protocols such as SSL/TLS.
Digital Modulation Techniques: PSK, FSK, QPSK, MSK, GMSK, M-ary Signaling
Digital Modulation Techniques
Phase Shift Keying (PSK)
PSK is a digital modulation technique that conveys data by changing the phase of a reference signal. It is widely used due to its robustness against noise.
Frequency Shift Keying (FSK)
FSK is a frequency modulation scheme that conveys digital information using discrete frequency changes. It is commonly used in various communication systems for its reliability.
Quadrature Phase Shift Keying (QPSK)
QPSK is a type of PSK that conveys two bits of data per symbol by utilizing four distinct phase shifts. This increases the data rate without requiring additional bandwidth.
Minimum Shift Keying (MSK)
MSK is a special type of FSK that maintains a constant envelope and has good spectral efficiency. It is often used in mobile communication systems.
Gaussian Minimum Shift Keying (GMSK)
GMSK is a variant of MSK that applies a Gaussian filter to the digital signal, improving bandwidth efficiency further while maintaining a constant envelope.
M-ary Signaling
M-ary signaling refers to a modulation technique where M distinct symbols are used to represent data. It allows more bits to be transmitted per symbol, increasing the data rate.
Spread Spectrum Techniques: DSSS and FHSS, Synchronization, Acquisition and Tracking
Spread Spectrum Techniques: DSSS and FHSS
Introduction to Spread Spectrum
Spread spectrum is a communication technique that spreads the signal over a wider bandwidth than necessary for the information being transmitted. This approach provides benefits such as resistance to interference, improved security, and the ability to share the frequency band with other users.
Direct Sequence Spread Spectrum (DSSS)
DSSS encodes data by modulating a data signal with a high-frequency code sequence (also known as a spreading code), which is usually a pseudo-random sequence. Each bit of the data signal is represented by multiple bits of the spreading code, which helps to spread the signal over a wider bandwidth. The advantages of DSSS include resistance to jamming and multipath fading, as well as improved signal detection through correlation.
Frequency Hopping Spread Spectrum (FHSS)
FHSS involves dividing the transmission frequency into multiple channels and hopping between them in a pseudo-random sequence. This rapid switching decreases the risk of interference, as the signal is only present on a channel for a short time. FHSS is robust against narrowband interference and eavesdropping.
Synchronization Techniques
Synchronization is crucial in spread spectrum systems to ensure that transmitters and receivers are correctly aligned in time. For DSSS, synchronization involves aligning the spreading code with the received signal. For FHSS, synchronization ensures that both transmitter and receiver are on the same frequency during transmission.
Acquisition and Tracking
Acquisition is the process of initially detecting and locking onto the signal, while tracking maintains this lock over time. In DSSS, acquisition techniques may include matched filtering to improve probability of detection. In FHSS, tracking involves monitoring the hopping pattern to stay synchronized with the transmitter.
