Basics of Hamming Distance

Duration: 8 min

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Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
  15. Paper 2 - Full-length Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces Hamming distance as a fundamental metric in coding theory, defining it as the number of differences between corresponding bits in two words of equal size. The instructor demonstrates calculation methods using XOR operations and bitwise comparison, then extends the concept to Minimum Hamming Distance within a set of codewords. Finally, the lesson establishes three critical parameters for coding schemes: codeword size n, dataword size k, and minimum Hamming distance dmin.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a definition of Hamming distance, denoted as d(x, y), representing the count of differing bits between two words. The instructor explains that applying an XOR operation on two binary words and counting the resulting 1s provides a quick calculation method. On-screen text explicitly states: 'The Hamming distance between two words (of the same size) is the number of differences between the corresponding bits.' A worked example demonstrates d(000, 011) equals 2 because the XOR result is 011, containing two 1s. The segment concludes by introducing a practice problem: 'The Hamming distance d(10101, 11110) is ________ ?' requiring students to apply the XOR method.

  2. 2:00 – 5:00 02:00-05:00

    The lecture transitions to Minimum Hamming Distance, defined as the smallest distance between any pair of codewords in a set. The instructor presents four binary codewords labeled C1 through C4 and systematically calculates pairwise distances to identify the minimum. Visible calculations include d(00000, 01011) = 3 and d(01011, 11110) = 3. The instructor writes these values on a whiteboard next to the slide content, showing d(01011, 10101) = 4 and d(00000, 11110) = 4. After evaluating all combinations, the instructor concludes that d_min equals 3, emphasizing that this value determines error detection and correction capabilities.

  3. 5:00 – 7:46 05:00-07:46

    The final section establishes three essential parameters for any coding scheme: codeword size n, dataword size k, and minimum Hamming distance dmin. The notation C(n, k) is introduced to describe these schemes. Two specific examples are displayed in tables mapping datawords to codewords: C(3, 2) with dmin=2 and C(5, 2) with dmin=3. The instructor points to specific rows in the dataword table and circles parameters n and k in formulas, highlighting how input datawords transform into output codewords. The slide text explicitly lists 'Three Parameters' and shows the relationship between input size, output size, and error resilience.

The lecture progresses logically from basic distance calculation to system-level parameters. First, Hamming distance is defined as a bit-counting metric solvable via XOR operations. Second, Minimum Hamming Distance is derived by comparing all codeword pairs in a set to find the smallest value. Third, these concepts are unified under three coding parameters: n (codeword size), k (dataword size), and dmin. The examples C(3, 2) with dmin=2 and C(5, 2) with dmin=3 illustrate how different configurations affect error handling. The visual evidence shows consistent use of binary strings, XOR logic, and tabular mappings to reinforce these relationships.

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