Network Codes Based on Symmetric Matrices

The key challenges of future wireless communication are improving data rate and quality of service. However, the challenges posed by having a large number of users such as power control, frequency synchronization and independently faded channels scales with the number of users. Cooperative communications is a candidate technology for high data rate and multi-user communications. In this paper, a new design of distributed network codes is introduced. These network codes are based on algebraic constructions in finite fields. Finite fields have an attractive feature of constraining transmit signal energy and is resilient to fading channels. The codes have high diversity and scale up with an arbitrary number of users. The codes are an alternative to Generalized Dynamic Network Codes without a restriction on the field size. Results are compared to theoretical evaluations and systems with similar configurations.