Passive optical network based on orthogonal frequency division multiplexing (OFDM-PON) exhibits excellent performance in optical access networks due to its greater resistance to fiber dispersion, high spectral efficiency and exibility on both multiple services and dynamic bandwidth allocation. The major elements of conventional OFDM communication system are two-dimensional (2-D) signal mapper and one-dimensional (1-D) inverse fast fourier transform (IFFT). Three dimensional (3-D) OFDM use the concept of 3-D signal mapper and 2-D IFFT. With 3-D OFDM, minimum Euclidean distance (MED) is increased which results in BER performance improvement. As bit error rate (BER) depends on minimum Euclidean distance (MED) which is 15.46 % more in case of 3-D OFDM as compared to 2-D OFDM. Forward error correction (FEC) coding is a technique where redundancy is added to original bit sequence to increase the reliability of communication system. In this paper, we propose and analytically analyze a new PON architecture based on 3-D OFDM with convolutional coding and Viterbi decoding and is compared with conventional 2-D OFDM under various system impairments for coherent optical orthogonal frequency division multiplexing (CO-OFDM) without using any optical dispersion compensation. Analytical result show that at BER of 10-9, there is 2.7 dB, 3.8 dB and 9.3 dB signal-to-noise ratio (SNR) gain with 3-D OFDM, 3-D OFDM combined with convolutional coding and Viterbi hard decision decoding (CC-HDD) and 3-D OFDM combined with convolutional coding and Viterbi soft decision decoding (CC-SDD) respectively as compared to 2-D OFDM-PON. At BER of 10-9, 3-D OFDM-PON with CC-HDD gives 2.8 dB improvement in optical budget for both upstream and downstream path and gives 5.7 dB improvement in optical budget using 3-D OFDM-PON combined with CC-SDD as compared to conventional OFDM-PON system.