Low-density parity-check (LDPC) decoders are a type of error-correction decoder that are used in communication systems to correct errors that occur during data transmission. LDPC decoders are based on a class of error-correcting codes that have a sparse parity-check matrix, which leads to efficient decoding algorithms. LDPC decoders have become popular in recent years due to their excellent error-correction performance and low complexity. They are used in a wide range of communication systems, including satellite communication, wireless communication, and optical communication. The decoding process in LDPC decoders involves iteratively updating the probability distributions of the information bits until a valid codeword is obtained. This process is typically performed using algorithms such as belief propagation or message passing. Overall, LDPC decoders are a key component of modern communication systems, helping to ensure reliable and efficient data transmission.