The prime necessity in communication system is utilizing the available bandwidth efficiently. Hence, compression of data to be sent over the link has become inevitable. In this paper, an algorithm for compressing hyperspectral space images based on ZigZag 3D-DCT (Discrete Cosine Transform) technique is proposed. This method converts 2D gray-scale images into a 3 dimensional cube formation of 8*8*8 pixels and is operated with DCT. Thereafter the quantization and zig-zag scanning processes are implemented. After completing the processes, the 1D data vector formed facilitates in achieving better compression using run-length coding. Also, in order to design a complete practical system, a suitable irregular LDPC encoder is implemented in order to mitigate losses present in communication link. The performance of the algorithm is verified by plotting various quality measurement graphs, and determining its dominance over standard JPEG.