Minimal Header Overhead for Random Linear Network Coding

The energy used to transmit a single bit of data between the devices in wireless networks is equal to the energy for performing hundreds of instructions in those devices. Thus the reduction of the data necessary to transmit, while keeping the same functionality of the employed algorithms is a formidable and challenging scientific task. We describe an algorithm called Small Set of Allowed Coefficients (SSAC) that produces the shortest header overhead in random linear network coding schemes compared with all other approaches reported in the literature. The header overhead length is 2 to 7 times shorter than the length achieved by related compression techniques. For example, SSAC algorithm compresses the length of the header overhead in a generation of 128 packets to 24 bits, while the closest best result achieved by an algorithm based on error correcting codes has a header overhead length of 84 bits in $GF(16)$ and 224 bits in $GF(256)$. We show that the header length in SSAC does not depend on the size of the finite field where the operations are performed, i.e., it just depends on the number of combined packets $m$.