On the Construction and Decoding of Concatenated Polar Codes

A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any $\epsilon > 0$, and total frame length $N$, the parameters of the scheme can be set such that the frame error probability is less than $2^{-N^{1-\epsilon}}$, while the scheme is still capacity achieving. This improves upon 2^{-N^{0.5-\eps}}, the frame error probability of Arikan's polar codes. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity

Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding

We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a multi-user successive cancellation decoder is deployed at the receiver. The encoding is done separately across the users and is independent of the target achievable rate. For the code construction, the positions of information bits and frozen bits for each of the users are decided jointly. This is done by treating the polar transformations across all the $m$ users as a single polar transformation with a certain \emph{polarization base}. We characterize the resolution of achievable rates on the dominant face of the uniform rate region in terms of the number of users $m$ and the length of the polarization base $L$. In particular, we prove that for any target rate on the dominant face, there exists an achievable rate, also on the dominant face, within the distance at most $\frac{(m-1)\sqrt{m}}{L}$ from the target rate. We then prove that the proposed MAC polar coding scheme achieves the whole uniform rate region with fine enough resolution by changing the decoding order in the multi-user successive cancellation decoder, as $L$ and the code block length $N$ grow large. The encoding and decoding complexities are $O(N \log N)$ and the asymptotic block error probability of $O(2^{-N^{0.5 - \epsilon}})$ is guaranteed. Examples of achievable rates for the $3$-user multiple access channel are provided

Hedging Diffusion Processes by Local Risk-Minimisation with Applications to Index Tracking

The solution to the problem of hedging contingent claims by local risk-minimisation has been considered in detail in Follmer and Sondermann (1986), Follmer and Schweizer (1991) and Schweizer (1991). However, given a stochastic process Xt and tau1 tau2, the strategy that is locally risk-minimising for Xtau1 is in general not locally risk-minimising for Xtau2. In the case of diffusion processes, this paper considers the problem of determining a strategy that is simultaneously locally risk-minimising for Xtau for all tau. That is, a strategy that is locally risk-minimising for the entire process Xt. The necessary and sufficient conditions under which this is possible are obtained, and applied to the problem of index tracking. In particular, a close connection between the local risk-minimising and the tracking error variance minimising strategies for index tracking is established, and leads to a simple criterion for the selection of optimal set of assets from which to form a tracker portfolio, as well as a value-at-risk type measure for the set of assets used.minimal martingale measure; local risk-minimisation; hedging; incomplete market; index tracking; portfolio selection

A new insight on induced-tribological behaviour of hypereutectic Al-Si alloys manufactured by selective laser melting

In this work, the tribological behaviour of selective laser melting (SLM) processed hypereutectic Al-Si alloy is investigated by the ball on disc test with focus on the effect of silicon content (18 and 50 wt %). Different from the conventional casted sample, the SLM processed sample shows an ultra-fine microstructure with silicon size inferior to 5 μm. Indeed, the SLM processed hypereutectic Al-Si alloy illustrates a pseudo-eutectic microstructure consisted by supersaturated Al(Si) and primary silicon. Both the SLM processed Al-18Si and Al-50Si presents low wear rate about of 7.0 and 8.1◊10−4 mm3/(N◊m) respectively. Moreover, the wear mechanisms of conventional casted and SLM processed hypereutectic Al-Si alloys are compared and discussed

Performance Testing and Analysis of Synchronous Reluctance Motor Utilizing Dual-phase Magnetic Material

While interior permanent magnet (1PM) machines have been considered the state-of-the art for traction motors, synchronous reluctance (SynRel) motors with advanced materials can provide a competitive alternative. 1PM machines typically utilize Neodymium 1ron Boron (NdFeB) permanent magnets, which pose an issue in terms of price, sustainability, demagnetization at higher operating temperatures, and uncontrolled generation. On the other hand, SynRel machines do not contain any magnets and are free from these issues. However, the absence of magnets as well the presence of bridges and centerposts limit the flux-weakening capability of a SynRel machine and limit the achievable constant power speed ratio (CPSR) without having to significantly oversize the machine and/or the power converter. 1n this paper, a new material referred to as the dual-phase magnetic material where nonmagnetic regions can be selectively introduced within each lamination will be evaluated for SynRel designs. The dual-phase feature of this material enables non-magnetic bridges and posts, eliminating one of the key limitations of the SynRel designs in terms of torque density and flux-weakening. This paper will present, the design, analysis and test results of an advanced proof-of-concept SynRel design utilizing dual-phase material with traction applications as the ultimate target application