Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels

The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper. The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair. An infomation-theoretic approach is utilized to analyze the minimal average data rate required to attain the quadratic performance when the channel imposes a known constant delay on the transmitted data. This infimum average data rate is shown to be lower bounded by minimizing the directed information rate across a set of LTI filters and an additive white Gaussian noise (AWGN) channel. It is demonstrated that the presence of time delay in the channel increases the data rate needed to achieve a certain level of performance. The applicability of the results is verified through a numerical example. In particular, we show by simulations that when the optimal filters are used but the AWGN channel (used in the lower bound) is replaced by a simple scalar uniform quantizer, the resulting operational data rates are at most around 0.3 bits above the lower bounds.Comment: A less-detailed version of this paper has been accepted for publication in the proceedings of ACC 201

The Divine Comedy at Corinth: Paul, Menander and the Rhetoric of Resurrection

This article asks how the New Comedy of Menander might have influenced Paul\u27s theological rhetoric in 1 Cor 5–15. An intertextual reading of Paul\u27s letter against the backdrop of Menander\u27s Samia reveals a number of shared topics, ethical concerns and dramatic characteristics. Paul\u27s citation of Menander\u27s Thais in 1 Cor 15.33 is part of this larger strategy to frame the struggles in Corinth within the ambit of Greek household ‘situation comedy’. Like Menander, Paul hybridises tragic and comic motifs throughout his epistle, inflecting the comedy of the Christ narrative with tragic examples of human misapprehension in this plea for ecclesial reconciliation

The Death of Tragedy: The Form of God in Paul’s \u3cem\u3eCarmen Christi\u3c/em\u3e and Euripides’ Bacchae

Scholarship on Phil 2:6–11 has long wrestled with the question of “interpretive staging.” While acknowledging that Jewish sapiential and apocalyptic literature as well as Roman apotheosis narratives provide important matrices for the hymn, the following study pinpoints a third backdrop against which Paul\u27s dramatic christology would have been heard in Philippi: Euripidean tragedy. Echoes of Dionysus\u27s opening monologue from Euripides\u27s Bacchae in the carmen Christi suggest that Roman hearers of Paul\u27s letter likely understood Christ\u27s kenotic metamorphosis as a species of Dionysian revelation. This interpretive recognition accomplishes a new integration of the hymn\u27s Jewish and imperial-cultic transcripts. Jesus\u27s Bacchic portraiture supports a theology of Christ\u27s pre-existence, while simultaneously establishing him as a Dionysian antithesis to the imperial Apollonian kyrios Caesar. These Dionysian echoes also elevate the status of slaves and women, and suggest that “the tragic” remains modally present within the otherwise comic fabula of the Christ myth

Capacity of a Class of Deterministic Relay Channels

The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y_1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R_0, is shown to be C(R_0) = \max_{p(x)} \min \{I(X;Y)+R_0, I(X;Y, Y_1) \}. Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, ``hash-and-forward'', is based on a simple yet novel use of random binning on the space of relay outputs, while the second scheme uses the usual ``compress-and-forward''. In fact, these two schemes can be combined together to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with rate-limited state information at the decoder in the special case when the channel state is recoverable from the channel input and the output.Comment: 17 pages, submitted to IEEE Transactions on Information Theor