Coding Theory Overview

A type of lossless data compression that uses a tree structure to represent the frequency of symbols in a message, assigning shorter codes to more frequent symbols. This results in compressed data with a smaller average number of bits per symbol.

A process of assigning variable-length codes to symbols based on their frequency of occurrence in a message. The code words are generated from a tree structure where nodes represent symbols and branches represent bits.

The process of reconstructing the original message from a compressed Huffman code string using the Huffman tree.

A method for quantifying the amount of information per symbol in a message. It is calculated using the base-2 logarithm of the number of possible symbols.

A measure of information in a message, calculated as the average number of bits per symbol in the compressed data. Lower entropy indicates better compression.

A type of entropy encoding that encodes an entire message as a single fractional value. It provides more efficient compression than Huffman coding, especially for messages with varying symbol frequencies.

The average number of bits used to represent a symbol in the compressed data.

A method for compressing data by defining probabilities for each symbol in the message and then encoding each symbol based on its probability, achieving greater efficiency over methods like Huffman coding.

Each symbol is represented by a variable-length code based on its probability of occurrence in the message, achieving greater compression than fixed-length encoding methods.

A special symbol indicating the end of a message, transmission, or file. It helps the decoder distinguish the end of the compressed data.

The process of converting a fractional arithmetic code into a decimal value.

A dynamic programming algorithm used to find the most likely sequence of hidden states in a system. It's commonly employed in decoding convolutional codes for various communication technologies.

A graphical representation of the possible states of a system and the transitions between them. Each node represents a state, and each edge represents a transition with a specific probability.

A measure of the difference between two binary strings. It counts the number of positions where the corresponding bits are different.

A type of digital modulation where data is encoded using convolutional codes. It efficiently transmits information over a noisy channel by introducing redundancy.

A type of code that utilizes memory by combining the current input bit with previous bits to produce the output. It provides error correction capabilities by introducing redundancy into the data stream.

Ensuring that only authorized individuals can access sensitive information. This is achieved through encryption, where data is transformed into an unreadable format, preventing unauthorized access.

Verifying that data has not been altered, corrupted, or tampered with. This involves using techniques such as checksums and digital signatures to detect any changes made to the data.

Verifying the identity and authenticity of individuals or devices involved in a communication. This ensures you are communicating with the intended party and not an imposter.

Preventing the sender of a message from denying that they sent it. This involves using techniques like digital signatures, ensuring accountability and preventing disputes.

Dividing a secret into multiple parts, each requiring a separate key to access. This ensures that the secret is only revealed if all the keys are combined.

The process of transforming data into an unreadable format using a secret key. It's like putting a lock on a treasure chest, but only the 'key' (encryption algorithm) can unlock it.

The process of reversing encryption, using a secret key to convert encrypted data back into its original format. It's unlocking the treasure chest with the right 'key' and retrieving the original content.

A type of encryption where the same key is used for both encryption and decryption. It's like using the same key to lock and unlock a door.

An encryption standard established by NIST in 2001, It is one of the most secure encryption methods currently available.

A type of encryption using a different key for encryption and decryption; each key is mathematically related but cannot be generated from one another.

A common asymmetric encryption algorithm named after its inventors: Ron Rivest, Adi Shamir, and Leonard Adleman. It is widely used for secure communication and digital signatures.

The encrypted message produced from applying an encryption algorithm.

A type of encryption that uses a long sequence of random-looking characters to disguise the original data.

An algorithm used to decode convolutional codes, finding the most likely sequence of states transmitted, by minimizing an accumulated distance metric (e.g., Hamming distance).

A diagram used to visualize the accumulation of Hamming distances between possible state transitions, aiding in Viterbi decoding by identifying the path with the least accumulated distance.

A technique that ensures only the intended recipient can view or decipher a message, using mathematical algorithms to encrypt and decrypt data.

A mathematical function used in cryptography to scramble and unscramble data, based on a specific key or algorithm.

A secret piece of information, often a string of characters, used to unlock encrypted data and recover the original message.