A perfect reconstruction paradigm for digital communication

A Remark on an Example By Teel–Hespanha With Applications to Cascaded Systems

“…However, when estimating the upper bound of the derivative of Lyapunov functional for systems with time-varying delay, there is room for investigation. For example, in [6], [10] On the other hand, some other efforts on improving the delay-dependent conditions were made through introducing new Lyapunov functionals [11] In this note, a new method that introduces the new free-weighting matrices is proposed to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms. Some less conservative delay-dependent stability criteria for systems with timevarying delay are presented by introducing new types of Lyapunov functionals.…”

Encoder-Decoder Design for Perfect Reconstruction: A Robust Control Perspective

“…Proof: The "if" part follows from the fact that the signals s and n are ∞ bounded (by 1 and b respectively) sequences and therefore Condition 1 guarantees that the soft error (Λ K s −s)(k) is always bounded away from 1 for all k. Henceŝ(k) = Θs(k) = s(k − K) for all time instants k ≥ K. The "only if part" can be essentially shown as in Proposition 3.1 of [3]; the details are omitted here for brevity. The implication of the above theorem is that the PR problem associated with the nonlinear system in Figure 1 is equivalent to checking Condition 1 in the linear system of Figure 2.…”

“…A DFE structure is assumed for the receiver while a linear transmitter structure is imposed together with the requirement that the power of the transmission is limited. Under these circumstances, we built on our previous framework and results [3], [4] to provide necessary and sufficient conditions for perfect reconstruction in terms of the 1 norms of appropriate maps. An 1 iteration procedure that results in parametric linear programs is developed to optimize the design parameters for the transmitter-receiver pair.…”

“…Designing a system that minimizes this probability is a hard problem and the proposed algorithms are characterized by high complexity (e.g., Viterbi's algorithm [1]). In our earlier works in [3], [4] we presented a deterministic worst-case framework for perfect reconstruction of discrete (source) data transmissions. Our framework is applicable to a number of applications where unknown but bounded noise models are more realistic than additive white Gaussian noise (AWGN) channels.…”

Synthesis of Simple Feed-Forward Networks: A First-Order Example

“…In this paper, we consider the simple feed-forward network, shown in Figure 2, in which a plant and controller are both remote and separated from the reference command by a discrete communication channel. There is much work that focuses on the reconstruction of the reference command at the remote site (see [18] and references therein). However, here we are interested in driving a remote system with the reconstructed command.…”