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.