Permuted Linear Model for Header-Free Communication via Symmetric Polynomials

We present a linear model with an unknown permutation matrix for header-free communication in massive Internet-of-Things (IoT) networks, thereby supporting low-latency communication. Besides the header-free communication application, the permuted linear model also has many applications in matching and correspondence estimation problems. To solve this permuted linear system, the key idea is to convert it into a system of polynomial equations via power sum symmetric polynomials. In our proposed method, specific assumptions (e.g., low-rankness and sparsity) about the permuted linear model is not needed. The closed form of the solution is established for a special case. Computational results show that the proposed method achieves good performance.