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.