Conventional error control schemes for wireless networks are inapplicable to multicast error control, as it is incapable of handling errors happening at multiple receivers simul-taneously. . In the wireless multicast environment, a single packet transmission can cause multiple packet losses. In that sense, the automatic repeat-request (ARQ) scheme, which has been commonly used for typical network error controls, is hardly applied to multicast applications.
In the recent researches for multicast error control, network coding is considered as one possible solution to overcome the conventional ARQ limitation in terms of correction efficiency. Network coding transmits error control packets in a form of a polynomial equation using linear combinations of a block of data packets, and then receiving stations retrieve errors from it using Gaussian elimination. Hence, multiple packet errors spread over different receivers can be efficiently retrieved by a single network coding error control packet.
However, these approaches have the following obstacles to be applied to practical net-works: 1) First, typically in multicast transmissions with ARQ, error reports, such as ACK and NACK, should be carefully managed to avoid error-report packet collisions and can be a big burden in a wireless environment. 2) Second, matrix inversion for network coding requires a high computational capacity of O($n^3$), where n is the rank of a correc-tion matrix.
According to the aforementioned schemes, the correction efficiency is the critical point to analyze the performance of a network error control scheme. Therefore, this thesis in-troduces the optimal point for the 2D network coding which is reliable against burst/multiple packet losses with low computational complexity. Since our proposed scheme does not use an error report packet and has no assumption for lossless control packet, it could be adopted for real network environment to achieve high correction effi-ciency in multicast ...