Abstract
The construction of polar codes with code length $n=2^m$ involves $m$ layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the polarization process. More precisely, if the previous bit is more reliable than its next bit under the successive decoder, then switching the decoding order of these two adjacent bits will make the reliable bit even more reliable and the noisy bit even noisier. Based on this observation, we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes. We add a permutation layer after each polar transform layer in the construction of the ABS polar codes. In order to choose which pairs of adjacent bits to swap in the permutation layers, we rely on a new polar transform that combines two independent channels with $4$-ary inputs. This new polar transform allows us to track the evolution of every pair of adjacent bits through different layers of polar transforms, and it also plays an essential role in the Successive Cancellation List (SCL) decoder for the ABS polar codes. Extensive simulation results show that ABS polar codes consistently outperform standard polar codes by 0.15dB--0.3dB when we use CRC-aided SCL decoder with list size $32$ for both codes. The implementations of all the algorithms in this paper are available at https://github.com/PlumJelly/ABS-Polar
Highlights
F AST and accurate numerical modeling is critical for the design and optimization of novel RF circuits and devices
We present a new fast frequency sweeping technique based on analytic extension of eigenvalues (AEE) for an efficient analysis of miniature passive RF circuits over a broad frequency band
We present the comparison between the quasi-static AEE and full-wave solutions for several testing problems to investigate the range of validity and errors of the AEE-based quasi-static analysis
Summary
F AST and accurate numerical modeling is critical for the design and optimization of novel RF circuits and devices. For RF circuits and devices, numerical methods such as the finite-element method (FEM) and the moment method (MoM), have been very well developed for accurate numerical modeling. They are most efficient when performing a single-frequency analysis; they become time consuming for a frequency sweep analysis over. To alleviate this problem, a variety of fast frequency sweeping techniques have been developed in the past, which were based on either physical or mathematical models
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