2.2.2.2.1 Basic Principles Used in the Encoding Technique
Treat k source packets as variables labeled xi...xk, where xi equals the numerical value of the ith packet. The variables are arranged as a vector, X, with k rows.

Figure 1: RTSP encoding variables and formula (source matrix)
From the linear algebra principle, any k linearly independent equations involving k number of variables can be solved to obtain the values for those variables. Now, consider an n * k generator matrix G, where each row in G specifies the coefficients of an equation. Multiplying G with the vector X results in k linear equations.
If the values of the variables in vector X are known, multiplying G and X results in the vector Y with n elements.

Figure 2: RTSP encoding variables and formula (generator matrix)
Given the vector Y and the generator matrix G, the original vector X can be recalculated, provided that any k rows of matrix G are linearly independent, that is, any submatrix formed by taking k rows of matrix G is invertible. Any k rows of the matrix G can be chosen to generate G'. The multiplication of the inverse of G' with vector Y will result in the original vector X.

Figure 3: RTSP encoding variables and formula (identity matrix for server, and inverse for client)