This project report details the design and analysis of a digital communication system, modeling the source output as a Bernoulli random process. The system employs a bi-orthogonal constellation with cardinality M=8. The report covers key aspects such as bandwidth efficiency, power efficiency, and the impact of AWGN noise. Monte Carlo simulations are used to evaluate symbol error probability, comparing results with theoretical bounds and nearest neighbor approximations. Gray coding is implemented to improve performance, and the report further explores the use of an extended (8,4) Hamming code for error correction, including Shannon bandwidth considerations and soft decoding techniques. The project incorporates MATLAB simulations and analysis, providing graphical illustrations of error probabilities and constellation diagrams. The study was conducted at Università Degli Studi Di Cassino E Del Lazio Meridionale.