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This paper deals with reduction of inter cellular interference in Multi-carrier communication systems. In the past, Load Matrix(LM) is proposed to allocate power to different users in a network based upon Signal to noise plus interference ratio (SNIR) so as to reduce inter cellular interference and is observed for single carrier systems. In Multi carrier systems the SNIR is affected distinctly in each carrier thus a single SNIR for power allocation is not optimal. In this paper, to obtain the optimization of power allocation in Multi-Carrier system, Load Matrix coding with bifurcated SNIR (LM-BFSNIR) is proposed. Using this approach it is observed that inter cellular interference is reduced better when compared to a single carrier system evaluated over a 3GPP-LTE standard.