Collision Codes: Decoding Superimposed BPSK Modulated Wireless Transmissions

The introduction of physical layer network coding gives rise to the concept of turning a collision of transmissions on a wireless channel useful. In the idea of physical layer network coding, two synchronized simultaneous packet transmissions are carefully encoded such that the superimposed transmission can be decoded to produce a packet which is identical to the bitwise binary sum of the two transmitted packets. This paper explores the decoding of superimposed transmission resulted by multiple synchronized simultaneous transmissions. We devise a coding scheme that achieves the identification of individual transmission from the synchronized superimposed transmission. A mathematical proof for the existence of such a coding scheme is given.