Error Correction Techniques

Error Correction

• Types of errors:
  • Bit-level errors: single-bit flip
  • Burst errors: multiple consecutive bits affected
• Error correction techniques:
  • Parity bits: single-bit parity (odd/even) and two-dimensional parity
  • Checksums: calculate and compare with received data
  • Cyclic redundancy checks (CRCs): polynomial-based error detection
  • Hamming codes: single-error correction and double-error detection
  • Reed-Solomon codes: block-based error correction

Binary Representation

• Binary number system:
  • Base 2, using only 0s and 1s
  • Can represent integers, fractions, and characters
• Binary encoding:
  • ASCII (American Standard Code for Information Interchange): 7-bit character encoding
  • Unicode: 16-bit and 32-bit character encoding
  • Binary-coded decimal (BCD): 4-bit encoding for decimal numbers

Encoding Schemes

• Line encoding:
  • Unipolar: single voltage level
  • Bipolar: two voltage levels (positive and negative)
  • Manchester: encoding with clock signal
• Block encoding:
  • Huffman coding: variable-length prefix codes
  • Lempel-Ziv-Welch (LZW) coding: dictionary-based compression
  • Run-length encoding (RLE): repeat-count encoding

Data Compression

• Lossless compression:
  • Huffman coding
  • LZW coding
  • RLE
  • Arithmetic coding
• Lossy compression:
  • Discrete cosine transform (DCT): image and video compression
  • Psychoacoustic models: audio compression
  • Fractal compression: image and video compression

Cryptography

• Types of cryptography:
  • Symmetric-key cryptography: same key for encryption and decryption
  • Asymmetric-key cryptography: public and private keys
• Ciphers:
  • Substitution ciphers: character substitution
  • Transposition ciphers: character rearrangement
  • Block ciphers: encrypting data in blocks
• Hash functions:
  • SHA (Secure Hash Algorithm): one-way encryption
  • MD5 (Message-Digest Algorithm 5): one-way encryption

Error Correction

• Bit-level errors occur when a single bit is flipped
• Burst errors affect multiple consecutive bits
• Parity bits can detect single-bit errors using odd or even parity
• Checksums are calculated and compared with received data to detect errors
• Cyclic redundancy checks (CRCs) use polynomials to detect errors
• Hamming codes can correct single-bit errors and detect double-bit errors
• Reed-Solomon codes correct errors in blocks of data

Binary Representation

• Binary number system is base 2, using only 0s and 1s
• Binary can represent integers, fractions, and characters
• ASCII is a 7-bit character encoding standard
• Unicode uses 16-bit and 32-bit character encoding
• Binary-coded decimal (BCD) uses 4-bit encoding for decimal numbers

Encoding Schemes

• Unipolar line encoding uses a single voltage level
• Bipolar line encoding uses two voltage levels (positive and negative)
• Manchester encoding combines data with a clock signal
• Huffman coding uses variable-length prefix codes
• Lempel-Ziv-Welch (LZW) coding uses dictionary-based compression
• Run-length encoding (RLE) uses repeat-count encoding

Data Compression

• Lossless compression methods include Huffman coding, LZW coding, RLE, and arithmetic coding
• Lossy compression methods include discrete cosine transform (DCT), psychoacoustic models, and fractal compression
• Discrete cosine transform (DCT) is used for image and video compression
• Psychoacoustic models are used for audio compression
• Fractal compression is used for image and video compression

Cryptography

• Symmetric-key cryptography uses the same key for encryption and decryption
• Asymmetric-key cryptography uses public and private keys
• Substitution ciphers substitute characters
• Transposition ciphers rearrange characters
• Block ciphers encrypt data in blocks
• SHA (Secure Hash Algorithm) is a one-way encryption hash function
• MD5 (Message-Digest Algorithm 5) is a one-way encryption hash function