Graph-based codes are a type of error-correction code that utilize graph theory in their design and encoding process. These codes are based on graphs, where nodes represent data bits and edges represent parity check constraints. By representing the code in a graphical form, graph-based codes offer a unique and efficient way to correct errors in communications systems. Graph-based codes have been widely studied and used in various applications such as wireless communication, storage systems, and digital transmission. They offer high error-correction capabilities, low decoding complexity, and good performance in noisy environments. Some popular examples of graph-based codes include low-density parity-check (LDPC) codes and turbo codes. LDPC codes, in particular, have gained significant attention due to their excellent error-correction performance and low complexity decoding algorithms. Overall, graph-based codes have proven to be effective and versatile in correcting errors in communication systems, making them a valuable area of research in the field of coding theory.