Problem
Research questions and friction points this paper is trying to address.
Linear Time-Invariant
Gaussian Channels
Power Constraints
Estimation Error Covariance
Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach
๐ค AI Summary
็ ็ฉถไบ้่ฟๅ้ฆ็ๅ็ๅ้ๅนถ่ก้ซๆฏไฟก้ไผ ่พ็ฆปๆฃๆถ้ดLTIๅ้ๆบ็ถๆ็้ฎ้ข๏ผๆๅบๅบไบไธปๅๆนๆณ็็บฟๆง็ผ็ ่งฃ็ ๅจ่ฎพ่ฎกใ
๐ Abstract
We study the design of linear time-invariant (LTI) encoder-decoder pairs for transmitting the state of a discrete-time LTI vector source over power-constrained parallel Gaussian channels with feedback. Two types of power constraints are considered. Under individual subchannel power constraints, a necessary and sufficient condition for designing an encoder-decoder pair that achieves bounded estimation error covariance (EEC) is established via two coupled majorization inequalities involving the subchannel signal-to-noise ratios and the antistable poles of the source. Under total channel power constraint, we derive the minimum total power required for a feasible encoder-decoder design by exploiting partial-order progamming under majorization order. An analytical optimal power allocation is obtained for the case of equal noise variances, which admits a water-filling interpretation; for general noise case, a sequential water-filling algorithm is developed. Our results reveal that the difficulty of transmitting a discrete-time LTI source via LTI coding is governed not only by its topological entropy, but also by the evenness of the log-magnitudes of its antistable poles. The design methods for feasible encoder-decoder pairs are also provided.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Majorization Inequalities
Antistable Poles
Water-Filling Algorithm
Power Allocation
Linear Time-Invariant (LTI) Coding
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