This book explains the following topics: Linear Codes, Probability
as Fancy Counting and the q-ary Entropy Function, Combinatorics, The Greatest
Code of Them All: Reed-Solomon Codes, What Happens When the Noise is Stochastic:
Shannon's Theorem, Bridging the Gap Between Shannon and Hamming: List Decoding,
Code Constructions, Code Concatenation, Algorithms, Decoding Concatenated Codes,
Efficiently Achieving the Capacity of the BSCp, Efficient Decoding of
Reed-Solomon Codes, Efficiently Achieving List Decoding Capacity, Applications.
Author(s): Venkatesan Guruswami, Atri Rudra and Madhu
Sudan
This note explains the
following topics: Text Compression, Error Detection and Correction,
Cryptography, Finite State Machines, Recursion and Induction, Relational
Database.
Coding theory includes the study of compression codes which enable us
to send messages cheaply and error correcting codes which ensure that messages
remain legible even in the presence of errors. Topics covered includes: Codes
and alphabets, Huffman’s algorithm, Shannon’s noiseless coding theorem , Hamming’s breakthrough, Shannon’s noisy coding theorem , Linear codes,
Polynomials and fields , Cyclic codes, Stream ciphers, Asymmetric systems,
Commutative public key systems, Trapdoors and signatures.
This note
covers the following topics: Introduction to programming, Use of objects and
variables, Definition of methods and classes, Primitive data types, Conditional
statements, Loop statements, Arrays and matrices, Files and input/output
streams, Program errors and exception handling, Recursion, Dynamic arrays and
linked lists.
This book has been written as
lecture notes for students who need a grasp of the basic principles of linear
codes. Topics covered includes: Shannon theory and coding, Coding theory,
Decoding of linear codes and MacWilliams identity, Coding theory - Constructing
New Codes, Coding theory - Bounds on Codes, Reed-Muller codes, Fast decoding of
RM codes and higher order RM codes.
This note introduces the theory of
error-correcting codes to computer scientists. This theory, dating back to the
works of Shannon and Hamming from the late 40's, overflows with theorems,
techniques, and notions of interest to theoretical computer scientists. The
course will focus on results of asymptotic or algorithmic significance.
Principal topics include: Construction and existence results for
error-correcting codes, Limitations on the combinatorial performance of
error-correcting codes, Decoding algorithms, Applications in computer science.
The
main focus of this book is the design process that leads from problem statements
to well-organized solutions; it deemphasizes the study of programming language
details, algorithmic minutiae, and specific application domains. It covers the
following topics: Processing Simple Forms of Data, Processing Arbitrarily Large
Data, Abstracting Designs, Generative Recursion, Accumulating Knowledge,
Changing the State of Variables, Changing Compound Values.
Author(s): Matthias
Felleisen, Robert Bruce Findler, Matthew Flatt and Shriram Krishnamurthi
This book covers the following
topics: Introduction to Programming,
General Computation Models, Declarative Programming Techniques, Declarative
Concurrency, Relational Programming, Object-Oriented Programming, Encapsulated
State, Concurrency and State, Specialized Computation Models, Semantics and
Virtual Machines.