Blind Construction of a Party Check Matrix for Arbitrary Linear Block Codes

Communication systems are systems in which a transmitter sends data across a channel to a receiver. In any modern communication system, Forward Error Correction (FEC) is used to detect and correct errors that occur during transmission. As communication systems have developed over the years, many FEC algorithms have been proposed. Each FEC algorithm has parameters that can be selected based on the needs of the communication system. Typically, the transmitter and receiver are both aware of the FEC parameters, but in some cases the receiver may not know how the transmitter encoded its message. In this case, the receiver must blindly determine the FEC parameters. This thesis offers a method to blindly recognize an important parameter of the FEC code, called a parity check matrix. The parity check matrix helps the receiver to decode the messages sent by the transmitter. The method described in this paper takes a noisy transmission and determines a parity check matrix without any prior knowledge of the FEC code. While the method outlined in this thesis does not work for every type of FEC code, it works for a category of FEC commonly used in modern communication systems called linear block codes.