📝 IPSec security services (12 MCQs)

📖 Explanation: The parameter D is the step size that determines how much the reconstructed value y_n changes each iteration. It multiplies the quantized direction q_n in the update rule $y_n = y_{n-1} + D \times q_n$, directly influencing the slope of the reconstructed signal.

📖 Explanation: When $e_n > 0$ the encoder decides to increase the reconstruction, so it sets the quantized direction $q_n$ to +1. This choice makes the decoder add $D$ in the next step, moving y_n upward toward the original signal.

📖 Explanation: The term $x_n - y_{n-1}$ measures the current mismatch between the true signal and its reconstruction. When this difference is quantized, the resulting q_n forces the decoder to add or subtract D, reducing the error in the next iteration and thus self‑correcting the trajectory.

📖 Explanation: Quantizing $x_n - y_{n-1}$ uses the previous reconstructed value y_{n-1} as a reference, so each update corrects the accumulated deviation. In contrast, quantizing the raw difference $x_n - x_{n-1}$ does not account for past reconstruction errors, allowing those errors to accumulate.

📖 Explanation: A large D causes the decoder to change y_n by a big amount each iteration. For a rapidly decreasing x_n, this can make y_n overshoot the true value, producing alternating large errors that grow rather than diminish, ultimately leading to instability in the reconstruction.

📖 Explanation: When C_n = 0 the encoder indicates a negative direction, so the decoder subtracts the step size. The update becomes $y_n = y_{n-1} - D$, moving the reconstructed value downward to follow a decreasing portion of the original signal.

📖 Explanation: Each iteration adds or subtracts 0.5, so y_n moves up half a unit then down half a unit, repeatedly. The net change over two steps is zero, keeping y_n confined to a narrow band. Thus the reconstruction oscillates but never grows without bound.

📖 Explanation: Using the update rule $y_n = y_{n-1} + D \times q_n$ (since C_n=1 indicates a positive direction), we compute $y_n = 3 + 2 \times (+1) = 5$. This moves the reconstruction upward toward the original signal.

📖 Explanation: Quantizing the difference between successive samples produces a step of fixed height D each time the ramp exceeds the previous step. Consequently the staircase trails the ideal linear ramp, creating a lag of roughly one quantization interval.

📖 Explanation: The error signal is defined as $e_n = x_n - y_{n-1}$. Without an initial reconstruction y_0, the first error cannot be calculated. Similarly, D determines how much y_n changes for each quantized direction, so both parameters are essential for accurate encoding.

📖 Explanation: A negative error indicates the reconstruction is above the true signal. With C_n = 0 the encoder signals a negative direction, so q_n is set to 0 (representing a negative step). The decoder then updates $y_n = y_{n-1} - D$, decreasing the reconstruction.

📖 Explanation: “Self‑correcting” means that each quantized update reduces the magnitude of the error. When $e_n$ is positive, q_n pushes y_n upward; when negative, it pushes downward. This feedback drives the subsequent error $e_{n+1}$ toward zero, gradually improving the reconstruction.