Low-density parity-check (LDPC) codes are a class of linear error-correcting codes that achieve near-optimal performance close to the Shannon limit, making them highly efficient for data transmission over noisy channels. They utilize sparse bipartite graphs for encoding and decoding, allowing for iterative algorithms that significantly reduce computational complexity.

Low-density Parity-check Codes

linear error-correcting codes

near-optimal performance

The Shannon Limit, also known as the Shannon Capacity, is a fundamental theorem in information theory that defines the maximum rate at which information can be transmitted over a communication channel without error, given the presence of noise. It establishes the theoretical boundary for data transmission efficiency, influencing the design of modern communication systems by highlighting the trade-off between bandwidth, noise, and data rate.

Shannon limit

Data transmission is the process of sending digital or analog data over a communication medium to one or more devices, ensuring accuracy and integrity during the transfer. It is fundamental to modern communication systems, enabling the exchange of information across networks and supporting various applications from internet browsing to telecommunication services.

data transmission

noisy channels

Sparse bipartite graphs are a type of graph characterized by having two disjoint sets of vertices with edges only between vertices of different sets, and a relatively low number of edges compared to the number of vertices. They are particularly useful in applications such as network flow optimization and matching problems due to their simplified structure and efficient computability.

sparse bipartite graphs

Encoding is the process of converting information into a different format using a specific scheme, facilitating storage, transmission, or interpretation by a receiving system. Decoding is the reverse process, transforming the encoded data back into its original format, enabling comprehension by humans or machines.

encoding and decoding

Iterative algorithms repeatedly apply a specific computational process to refine an approximation or solution, often converging towards an optimal result over successive iterations. They are fundamental in fields like numerical analysis, optimization, and machine learning, where exact solutions are difficult or impossible to obtain analytically.

iterative algorithms

Computational complexity is a branch of computer science that studies the resources required for algorithms to solve problems, focusing on time and space as primary metrics. It categorizes problems based on their inherent difficulty and the efficiency of the best possible algorithms that solve them, providing a framework for understanding what can be computed feasibly.

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