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The exhaustive list of topics in Coding Theory in which we provide Help with Homework Assignments and Help with Projects is as follows:

  • Linear Block Codes :
    • Coding Theory.
    • Linear Block Codes.
    • Generator Matrices.
    • Linear Block Codes.
    • Parity check matrices.
    • Vector space view of codes.
    • Dual codes.
    • Dual Codes.
    • Self-orthogonal and Self-Dual codes.
    • Examples of dual codes.
    • Relation between parity-check matrix and dual code.
    • Minimum Distance Decoder.
    • Hamming Distance.
    • Error Correcting Capability of codes.
    • Geometric View of Decoding.
    • Syndrome Decoder.
    • Relationship between Minimum distance and Parity-Check Matrix.
    • Construction of Codes with d=3.
    • Hamming Codes.
    • Extending codes.
    • Puncturing Codes.
    • Shortening codes.
    • Hamming bound.
    • Singleton bound.
    • Gilbert-Varshamov bound.
  • Finite Fields :
    • Groups.
    • Order of group elements.
    • Fermat's Little theorem.
    • Finite fields.
    • Polynomials over fields.
    • Polynomial Division.
    • Polynomial factorization over a field.
    • Irreducible polynomials.
    • Existence and construction of fields of a given size.
    • Finite field construction.
    • Power notation.
    • Primitives and primitive polynomials.
  • Codes over Finite Fields (BCH and RS codes) :
    • BCH codes.
    • Construction of BCH codes for given minimum distance.
    • Vandermonde matrices.
    • BCH bound.
    • Properties of BCH codes (cyclic).
    • Representation as polynomials.
    • Minimum polynomials.
    • Minimum polynomials.
    • Construction and properties.
    • Connection with cyclic codes.
    • Generator polynomial of a cyclic code.
    • Dimension of BCH codes.
    • Examples of BCH codes.
    • Systematic encoding.
    • Syndrome decoding for BCH codes.
    • Error Locators.
    • Reed-Solomon (RS) Codes.
    • Dimension.
    • Definition of distance.
    • Weight in GF(2^m).
    • Generator polynomial.
    • Minimum distance and binary expansion of RS codes.
    • Reed-Solomon (RS) Codes :
    • Decoding overview.
    • PGZ decoder for RS codes.
    • Reed-Solomon codes in practice :
    • Erasure decoding.
    • Burst erasure correction.
    • Modern decoders.
  • Coding Over AWGN channels :
    • AWGN channels.
    • Coding gain.
    • Encoding and decoding in AWGN channels.
    • Bitwise MAP Decoder.
    • Likelihood ratios.
    • LLRs.
    • ML and Map decoding for Repetition codes.
    • Probability of decoding error.
    • Channel Capacity.
    • Capacity for various schemes.
    • Eb/No.
    • Coding Gain.
    • Coding gain performances of previously studied codes.
    • Proof of capacity and random codes.
    • Low-Density Parity check (LDPC) codes.
    • Regular LDPC codes.
    • Gallager construction of LDPC codes.
  • LDPC codes :
    • Socket construction of regular LDPC codes.
    • Tanner Graphs.
    • Neighbourhoods and cycles in graphs.
    • Gallager A decoding algorithm for LDPC codes and its analysis.
    • LDPC Threshold.
    • Simulation of Gallager decoding.
    • Neighbourhood view of Gallager A decoding algorithm.
    • Simulation.
    • Irregular LDPC codes.
    • Node and edge perspective.
    • Gallager-A decoder on irregular LDPC codes.
    • Degree optimisation to achieve higher thresholds.
    • Soft-decision Message Passing Decoder for AWGN channels.
    • Soft-decision Message Passing Decoder for AWGN channels.
    • Density evolution for AWGN channels.
    • Density evolution for AWGN channels.
    • LDPC codes.
  • Convolutional codes and turbo codes :
    • Convolutional codes- Feedforward Convolutional Encoder.
    • Trellis Representation.
    • Viterbi Decoder for convolutional codes.
    • Recursive convolutional encoders.
    • Puncturing.
    • Turbo encoders.
    • Free distance of convolutional codes.
    • Trellises for block codes.
    • Code concatenation.
  • LDPC/Turbo codes in the wireless standards :
    • Turbo codes in the WiMax/3GPP standards.
    • Permutation polynomial interleavers.
    • LDPC codes in the WiMax standard.
    • Protograph LDPC codes and their properties.
    • Implementation aspects of turbo codes :
    • MAP decoder and MAXLOGMAP decoder for convolutional codes.
    • Design and architecture.
    • Implementation aspects of LDPC codes :
    • Tanh processing versus minsum decoder.
    • Design and architecture.