Getting Started What Is the Communications Toolbox? Expected Background Studying Components of a Communication System Modulating a Random Signal Plotting Signal Constellations Pulse Shaping Using a Raised Cosine Filter Using a Convolutional Code Simulating a Communication System Using BERTool to Run Simulations Varying Parameters and Managing a Set of Simulations Learning More Online Help Demos The MathWorks Online Examples Signal Sources White Gaussian Noise Random Symbols Random Integers Random Bit Error Patterns Performance Evaluation Performance Results via Simulation Using Simulated Data to Compute Bit and Symbol Error Rates Example: Computing Error Rates Comparison of Symbol Error Rate and Bit Error Rate Performance Results via the Semianalytic Technique When to Use the Semianalytic Technique Procedure for the Semianalytic Technique Example: Using the Semianalytic Technique Theoretical Performance Results Plotting Theoretical Error Rates Comparing Theoretical and Empirical Error Rates Error Rate Plots Creating Error Rate Plots Using semilogy Curve Fitting for Error Rate Plots Example: Curve Fitting for an Error Rate Plot Eye Diagrams Example: Eye Diagrams Scatter Plots Example: Scatter Plots Selected Bibliography for Performance Evaluation BERTool: A Bit Error Rate Analysis GUI Summary of Features Opening BERTool The BERTool Environment Components of BERTool Interaction Among BERTool Components Computing Theoretical BERs Example: Using the Theoretical Panel in BERTool Available Sets of Theoretical BER Data Using the Semianalytic Technique to Compute BERs Example: Using the Semianalytic Panel in BERTool Procedure for Using the Semianalytic Panel in BERTool Running MATLAB Simulations Example: Using a MATLAB Simulation with BERTool Varying the Stopping Criteria Plotting Confidence Intervals Fitting BER Points to a Curve Preparing Simulation Functions for Use with BERTool Requirements for Functions Template for a Simulation Function Example: Preparing a Simulation Function for Use with BERTool Running Simulink Simulations Example: Using a Simulink Model with BERTool Varying the Stopping Criteria Preparing Simulink Models for Use with BERTool Requirements for Models Tips for Preparing Models Example: Preparing a Model for Use with BERTool Managing BER Data Exporting Data Sets or BERTool Sessions Importing Data Sets or BERTool Sessions Managing Data in the Data Viewer Source Coding Quantizing a Signal Representing Partitions Representing Codebooks Scalar Quantization Example 1 Scalar Quantization Example 2 Determining Which Interval Each Input Is In Optimizing Quantization Parameters Example: Optimizing Quantization Parameters Differential Pulse Code Modulation DPCM Terminology Representing Predictors Example: DPCM Encoding and Decoding Optimizing DPCM Parameters Example: Comparing Optimized and Nonoptimized DPCM Parameters Companding a Signal Example: A µ-Law Compander Huffman Coding Creating a Huffman Code Dictionary Example: Creating and Decoding a Huffman Code Arithmetic Coding Representing Arithmetic Coding Parameters Example: Creating and Decoding an Arithmetic Code Selected Bibliography for Source Coding Error-Control Coding Block Coding Block Coding Features of the Toolbox Block Coding Terminology Representing Words for Reed-Solomon Codes Parameters for Reed-Solomon Codes Creating and Decoding Reed-Solomon Codes Representing Words for BCH Codes Parameters for BCH Codes Creating and Decoding BCH Codes Representing Words for Linear Block Codes Parameters for Linear Block Codes Creating and Decoding Linear Block Codes Performing Other Block Code Tasks Selected Bibliography for Block Coding Convolutional Coding Convolutional Coding Features of the Toolbox Polynomial Description of a Convolutional Encoder Trellis Description of a Convolutional Encoder Creating and Decoding Convolutional Codes Examples of Convolutional Coding Selected Bibliography for Convolutional Coding Interleaving Block Interleavers Block Interleaving Features of the Toolbox Example: Block Interleavers Convolutional Interleavers Convolutional Interleaving Features of the Toolbox Example: Convolutional Interleavers Delays of Convolutional Interleavers Selected Bibliography for Interleaving Modulation Modulation Features of the Toolbox Baseband Versus Passband Simulation Modulation Terminology Analog Modulation Representing Analog Signals Analog Modulation Example Digital Modulation Representing Digital Signals Baseband Modulated Signals Defined Examples of Digital Modulation and Demodulation Plotting Signal Constellations Selected Bibliography for Modulation Special Filters Noncausality and the Group Delay Parameter Example: Compensating for Group Delays When Analyzing Data Designing Hilbert Transform Filters Example with Default Parameters Filtering with Raised Cosine Filters Sampling Rates Designing Filters Automatically Specifying Filters Using Input Arguments Controlling the Rolloff Factor Controlling the Group Delay Combining Two Square-Root Raised Cosine Filters Designing Raised Cosine Filters Sampling Rates Example Designing a Square-Root Raised Cosine Filter Other Options in Filter Design Selected Bibliography for Special Filters Channels Channel Features of the Toolbox AWGN Channel Describing the Noise Level of an AWGN Channel Fading Channels Overview of Fading Channels Specifying Fading Channels Configuring Channel Objects Using Fading Channels Examples Using Fading Channels Using the Channel Visualization Tool Binary Symmetric Channel Example: Introducing Noise in a Convolutional Code Selected Bibliography for Channels Equalizers Equalizer Features of the Toolbox Overview of Adaptive Equalizer Classes Symbol-Spaced Equalizers Fractionally Spaced Equalizers Decision-Feedback Equalizers Using Adaptive Equalizer Functions and Objects Basic Procedure for Equalizing a Signal Example Illustrating the Basic Procedure Learning More About Adaptive Equalizer Functions Specifying an Adaptive Algorithm Choosing an Adaptive Algorithm Indicating a Choice of Adaptive Algorithm Accessing Properties of an Adaptive Algorithm Specifying an Adaptive Equalizer Defining an Equalizer Object Accessing Properties of an Equalizer Using Adaptive Equalizers Equalizing Using a Training Sequence Equalizing in Decision-Directed Mode Delays from Equalization Equalizing Using a Loop Using MLSE Equalizers Equalizing a Vector Signal Equalizing in Continuous Operation Mode Using a Preamble or Postamble Selected Bibliography for Equalizers Galois Field Computations Galois Field Terminology Representing Elements of Galois Fields Creating a Galois Array Example: Creating Galois Field Variables Example: Representing Elements of GF(8) How Integers Correspond to Galois Field Elements Example: Representing a Primitive Element Primitive Polynomials and Element Representations Arithmetic in Galois Fields Example: Addition and Subtraction Example: Multiplication Example: Division Example: Exponentiation Example: Elementwise Logarithm Logical Operations in Galois Fields Testing for Equality Testing for Nonzero Values Matrix Manipulation in Galois Fields Basic Manipulations of Galois Arrays Basic Information About Galois Arrays Linear Algebra in Galois Fields Inverting Matrices and Computing Determinants Computing Ranks Factoring Square Matrices Solving Linear Equations Signal Processing Operations in Galois Fields Filtering Convolution Discrete Fourier Transform Polynomials over Galois Fields Addition and Subtraction of Polynomials Multiplication and Division of Polynomials Evaluating Polynomials Roots of Polynomials Roots of Binary Polynomials Minimal Polynomials Manipulating Galois Variables Determining Whether a Variable Is a Galois Array Extracting Information from a Galois Array Speed and Nondefault Primitive Polynomials Selected Bibliography for Galois Fields Galois Fields of Odd Characteristic Galois Field Terminology Representing Elements of Galois Fields Exponential Format Polynomial Format List of All Elements of a Galois Field Nonuniqueness of Representations Default Primitive Polynomials Converting and Simplifying Element Formats Converting to Simplest Polynomial Format Example: Generating a List of Galois Field Elements Converting to Simplest Exponential Format Arithmetic in Galois Fields Arithmetic in Prime Fields Arithmetic in Extension Fields Polynomials over Prime Fields Cosmetic Changes of Polynomials Polynomial Arithmetic Characterization of Polynomials Roots of Polynomials Other Galois Field Functions Selected Bibliography for Galois Fields Functions - Categorical List Signal Sources Performance Evaluation Source Coding Error-Control Coding Interleaving/Deinterleaving Analog Modulation/Demodulation Digital Modulation/Demodulation Pulse Shaping Special Filters Lower-Level Functions for Special Filters Channels Equalizers Galois Field Computations Computations in Galois Fields of Odd Characteristic Utilities Graphical User Interface Functions - Alphabetical List