Error Control Coding

Unit 1

Context for Error Correction Coding: Introduction: Where Are Codes? , The Communications System, Basic Digital Communications , Signal Detection, Memoryless Channels , Simulation and Energy Considerations for Coded Signals, Hamming Codes

Unit 2

Linear Block Codes: Basic Definitions, The Generator Matrix Description of Linear Block Codes, The Parity Check Matrix and Dual Codes, Some Simple Bounds on Block Codes, Error Detection and Correction over Hard-Input Channels, Weight Distributions of Codes and Their Duals, Hamming Codes and Their Duals, Performance of Linear Codes

Unit 3

Cyclic Codes, Rings, and Polynomials: Introduction, Basic Definitions, rings, Quotient Rings, Ideals in Rings, Algebraic Description of Cyclic Codes, Nonsystematic Encoding and Parity Check, Systematic Encoding, Cyclic Encoding, Syndrome Decoding, Binary CRC Codes

Unit 4

Convolutional Codes: Definition of Codes and Equivalent Code, Decoding Convolutional Codes, Some Performance Results, Error Analysis for Convolutional Codes, Puncturing, Suboptimal Decoding Algorithms forConvolutionalCodes, Convolutional Codes as Block Codes, Trellis Representations of Block and Cyclic Codes .