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In this paper, we propose the two-stage constructions for the rate-compatible shortened polar (RCSP) codes. For the Stage-I construction, the shortening pattern and the frozen bit are jointly designed to make the shortened bits be completely known by the decoder. Besides, a distance-greedy algorithm is presented to improve the minimum Hamming distance of the codes. To design the remaining Stage-II frozen bits, three different construction algorithms are further presented, called the Reed-Muller (RM) construction, the Gaussian Approximation (GA) construction, and the RM-GA construction. Then we give the row weight distribution numerical results of the generator matrix after the Stage-I and Stage-II constructions, which shows that the proposed constructions can efficiently increase the minimum Hamming distance. Simulation results show that the proposed RCSP codes have excellent frame error rate (FER) performances at different code lengths and code rates. More specifically, the RM-GA construction performs best and can achieve at most 0.8 dB gain compared to the Wang14 and the quasi-uniform puncturing (QUP) schemes. The RM construction is designed completely by the distance-constraint without channel evaluation thus has the simplest structure. Interestingly, it still has better FER performance than the existing shortening/puncturing schemes, especially at high signal noise ratio (SNR) region.

Polar coding are the first class of provable capacity-achieving coding techniques for a wide range of channels. With an ideal recursive structure and many elegant mathematical properties, polar codes are inherently implemented with low complexity encoding and decoding algorithms. Since the block length of the original polar construction is limited to powers of two, rate-compatible polar codes (RCPC) are presented to meet the flexible length/rate transmission requirements in practice. The RCPC codes are well-conditioned to combine with the hybrid automatic repeat request (HARQ) system, providing high throughput efficiency and such RCPC-HAPQ scheme is commonly used in delay-insensitive communication system. This paper first gives a survey of both the classical and state-of-the-art encoding/decoding algorithms for polar codes. Then the RCPC construction methods are discussed, including the puncturing, shortening, multi-kernel construction, etc. Finally, we investigate several RCPC-HARQ jointly design systems and discuss their encoding gain and re-transmission diversity gain.

Low-cost, short-range optical interconnect technology plays an indispensable role in high-speed board-level data communications. In general, 3D printing technology can easily and quickly produce optical components with free-form shapes, while the traditional manufacturing process is complicated and time-consuming. Here, we present a direct ink writing 3D-printing technology to fabricate optical waveguides for optical interconnects. The waveguide core is 3D printed optical polymethylmethacrylate (PMMA) polymer, with propagation loss of 0.21 dB/cm at 980 nm, 0.42 dB/cm at 1310 nm, and 1.08 dB/cm at 1550 nm, respectively. Furthermore, a high-density multilayer waveguide arrays, including a four-layer waveguide arrays with a total of 144 waveguide channels, is demonstrated. Error-free data transmission at 30 Gb/s is achieved for each waveguide channel, indicating that the printing method can produce optical waveguides with excellent optical transmission performance. We believe this simple, low-cost, highly flexible, and environmentally friendly method has great potential for high-speed short-range optical interconnects.

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