The Polar Code and Telemedicine

One result of a warmer global climate is increased maritime activity in the Arctic. Areas that used to be covered by ice and snow are now accessible for the scientific community and commercial users. The Norwegian government has chosen tourism as a pillar of the economy of Svalbard and facilitates the development of the tourism industry. Aase and Jabour have shown that tourist vessels sail as far north as 82° N, beyond the range of geostationary satellites. The Polar Code states that appropriate communication equipment to enable telemedical assistance in polar areas shall be provided. This paper describes a series of functional telemedicine tests carried out on board the Norwegian Coast Guard vessel NoCGV Svalbard during her transit between Svalbard and the Norwegian mainland in September 2019. Communication was established between the vessel and Haukeland University Hospital in Bergen, Norway, using the new Iridium NEXT constellation of communication satellites. Our tests show that medical services that require low bandwidths work.

New Russian Legislative Approaches and Navigational Rights within the Northern Sea Route

The regulation of foreign navigation in the Northern Sea Route (NSR) has been dominated by the rules of international law applicable to merchant ships only. Neither the domestic set of rules of navigation on the NSR, based on Article 234 of UNCLOS nor the Polar Code applies to State-owned vessels. While the application of Article 234 has so far let Russia evade discussion on the navigational rights, one can expect an increasing spotlight on this issue. In response to the recent crossing of the NSR by a French warship, as well as the voices from the United States indicating similar plans, Russia has signalled the intention to adopt more stringent rules for passage of warships, potentially including the requirement of prior notification and pilotage. The aim of the paper is twofold. First, examine the navigational rights as applicable in the NSR. As such, the paper will discuss historical State practice and relevant international law to demonstrate, among other things, that the enclosure with straight baselines preserved innocent passage in all Russian Arctic straits. Second, examine the international legality of prior notification and pilotage in the context of the applicable navigational rights on the NSR.

Internal pilot insertion for polar codes

Two internal pilot insertion methods are proposed for polar codes to improve their error correction performance. The presented methods are based on a study of the weight distribution of the given polar code. The insertion of pilot bits provided a new way to control the coding rate of the modified polar code on the basis of the Hamming weight properties without sacrificing the code construction and the related channel condition. Rate control is highly demanded by 5G channel coding schemes. Two short-length polar codes were considered in the work with successive cancellation list decoding. The results showed that advantages in the range of 0.1 to 0.75 dB were obtained in the relative tolerance of the modified coded signal to the additive white Gaussian noise and fading channels at a bit error rate of 10⁻⁴. The simulation results also revealed that the performance improvements were possible with a careful insertion of the pilots. The modified polar code with pilot insertion provided performance improvement and offered the control of the coding rate without any added complexity at both the encoder and the decoder.

Multilevel polarization for quantum Channels

Recently, a purely quantum version of polar codes has been proposed in~\cite{DGMS19} based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as a channel combining operation. Here, we consider the quantum polar code construction using the same channel combining and splitting procedure as in~\cite{DGMS19}, but with a fixed two-qubit Clifford unitary. For the family of Pauli channels, we show that polarization happens in multi-levels, where synthesized quantum virtual channels tend to become completely noisy, half-noisy, or noiseless. Further, we present a quantum polar code exploiting the multilevel nature of polarization, and provide an efficient decoding for this code. We show that half-noisy channels can be frozen by fixing their inputs in either the amplitude or the phase basis, which allows reducing the number of preshared EPR pairs compared to the construction in~\cite{DGMS19}. We provide an upper bound on the number of preshared EPR pairs, which is an equality in the case of the quantum erasure channel. To improve the speed of polarization, we propose an alternative construction, which again polarizes in multi-levels, and the previous upper bound on the number of preshared EPR pairs also holds. For a quantum erasure channel, we confirm by numerical analysis that the multilevel polarization happens relatively faster for the alternative construction.