Basics of Hamming Distance

Duration: 8 min

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Module outline

  1. Quantitative Ability: Percentage, Profit and Loss, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Simple Interest and Compound Interest, Age Problems, Number System, Divisibility Rules, HCF LCM, Algebra, Permutation and Combination, Probability, Data Interpretation, Logarithm, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Speed Mathematics and Basic Mathematics
  2. Logical Reasoning: Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Data Sufficiency, Venn Diagram, Inequality, Series (Number and Letter Series) (Numerical Relations and Reasoning), Logical Sequence Of Words, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Subject Verb Agreement (Verb Noun Agreement), Tenses, Articles, Preposition, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Vocabulary, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Sentence Correction (Error Correction), Cloze Test (Cloze Passage), Facts, Inference and Judgements
  4. Programming Fundamentals (Technical): C Fundamentals
  5. Data Structures (Technical): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  6. Algorithms (Technical): Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis, Advanced Algorithms
  7. OOPs (Technical): Object Oriented Programming (OOPS)
  8. DBMS (Technical): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  9. SQL (Technical): SQL
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  11. Computer Networks (Technical): Introduction to CN, Data Communication, 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, Network Security, Cloud Computing and IoT, Cyber and Info Security
  12. Software Engineering (Technical): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Coding/Automata Round: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir, Pseudo Codes
  14. Personality / Behavioral Assessment: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
  15. Writing Assessment: English Writing Ability
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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