Communication with Crystal-Free Radios

Abstract

We consider a communication channel where there is no common clock between the transmitter and the receiver. This is motivated by the recent interest in building system-onchip radios for Internet of Things applications, which cannot rely on crystal oscillators for accurate timing. We identify two types of clock uncertainty in such systems: timing jitter, which occurs at a time scale faster than the communication duration (or equivalently blocklength); and clock drift, which occurs at a slower time scale. We study the zero-error capacity under both types of timing imperfections, and obtain optimal zeroerror codes for some cases. Our results show that, as opposed to common practice, in the presence of clock drift it is highly suboptimal to try to learn and track the clock frequency at the receiver; rather, one can design codes that come close to the performance of perfectly synchronous communication systems without any clock synchronization at the receiver.Index Terms-Asynchronous communication, clock drift, jitter, crystal-free radios 1 The width of the transmitted pulse is much shorter than the duration of the bin in [9].

Signaling to Relativistic Observers: An Einstein-Shannon-Riemann Encounter

“…In closing, we note that problems related to the one studied in this letter are also of interest in communication engineering, where they have been explored in the context of synchronization errors such as the so-called clock-drift; see, e.g., [9,10]. * kmladen@uns.ac.rs…”

“…Optimal codes for a model equivalent to ours (where, instead of relativistic time dilation, the signal distortion is caused by the so-called "clock drift") have been determined in [9] for the cases γ ∈ [1, γ] and γ ∈ [1, ∞). We next describe these codes, as well as the optimal codes for the remaining cases γ ∈ [1, γ), γ ∈ (1, γ), and γ ∈ (1, γ],…”

“…where b n C N,k stands for b n t : t ∈ C N,k , and the notation ∪ • emphasizes that the union in question is a disjoint union. The proof that B N,k is an optimal code for the model γ ∈ [1, γ] was given in [9], and is an application of the method of Shannon based on the so-called "adjacency-reducing mappings" [8, Thm 3]. The idea behind the construction of this code is similar to the idea for the case γ = ∞, except that now not all points on a given line through the origin are confusable.…”

Dynamic Channel Calibration on a Crystal-Free Mote-on-a-Chip

“…Application domains include activity trackers, wearables, smart materials, factory automation, in-body and personal health monitoring, and microrobots. To be able to scale to trillions of deployed wireless devices [1], they need to be small and cheap. This is the primary motivation for designing radios that do not require any external components [2].…”

“…Wireless communication systems (''radio chips'') have been demonstrated that are as small as 0.46 mm 2 [14], 2.025 mm 2 [15], ≈ 4.4 mm 2 [16], ≈9 mm 2 [17]. As a point of comparison, the area occupied by a small crystal oscillator is ≈2 mm 2 [1], [4].…”