Nonanticipative transmission for sources and channels with memory

Generalizations of Nonanticipative Rate Distortion Function to Multivariate Nonstationary Gaussian Autoregressive Processes

“…The nonanticipatory epsilon entropy of Gauss-Markov processes subject to a point-wise distortion is analyzed extensively in the literature, under various names, such as sequential, nonanticipative RDF (see, for example, [3]- [5]). In [3]- [5] various applications are identified, that include control of linear Gaussian control systems over memoryless communication channels with finite transmission rates [3], bounds on the optimal performance theoretically attainable by noncausal and causal codes [4], filtering subject to a fidelity [5], and joint source and channel coding and decoding design that operate in real-time [6]. In view of the difficulty to characterize finite-time NRDF and to compute its value, recently semidefinite programming is proposed to compute numerically its value for multivariate Gauss-Markov sources subject to a point-wise distortion [7].…”

Optimal Estimation via Nonanticipative Rate Distortion Function and Applications to Time-Varying Gauss--Markov Processes

“…For example, Derpich and Østergaard in [17] applied the nonanticipatory -entropy of the scalar Gaussian process subject to a MSE fidelity constraint, to derive several bounds on the OPTA by causal and zero-delay codes. Kourtellaris et al in [18] illustrated the simplicity of jointly designing an {encoder, channel, decoder} operating optimally in real-time, for a Binary Symmetric Markov process subject to a Hamming distance distortion function, which is communicated over a finite state channel with unit memory on past channel outputs (with some symmetry) subject to a transmission cost constraint. The NRDF is also applied in control-related problems using zero-delay communication constraints.…”

“…Kn e s||kn−kn|| 2 2 λ n (k n ,k n−1 )p(k n |k n−1 )dk n ≤ 1 , (B. 18) wherep(k n |k n−1 ) denotes the conditional density of k n given (k n−1 ). Take λ n (k n ,k n−1 ) ∈ Ψ n s such that λ n (k n ,k n−1 ) = α n p(k n |k n−1 ) (B.…”

Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes

“…Also, an information theoretic source-channel matching type argument can be made for special scenarios where the sequential rate-distortion [19] [20] achieving channel kernels are realized with the physical channel itself, a crucial case being the scalar Gaussian source transmitted over a scalar Gaussian channel under power constraints at the encoder [21]. Along this direction, a more modern treatment and further results are given in [22] and [23]. Optimal zero delay coding of Markov sources over noisy channels without feedback was considered in [16] and [24].…”