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In recent years, evolution of technology has contributed a major role in the field of optical communication systems. There is an ever growing demand for transmitting signals at higher data rates and compensating the transmission impairments simultaneously. Speed of the signal transmission down the optical fiber is limited by transmission impairments that are characterized as linear or nonlinear losses. In my thesis, I lay a special emphasis on linear loss especially chromatic dispersion and it's effect on an optical signal down the fiber and study the compensation techniques in an electrical domain challenging the methods employed in an optical domain. In this digital world, there is an increase in the evolution of electrical components such as high speed memory units and low power consumption models. Electrical domain provides advantages in terms of processing the signal in a cost effective way and achieving the similar results with respect to the optical domain. In addition to the analysis, my investigation includes the effect of noise present in optical fiber communication systems and limitations of electrical components in achieving the compensation.