SSRFSC flipping decoding algorithm based on critical simplification set for polar codes

To improve the decoding performance of the simplified sequence repetition node-based fast successive cancellation (SSRFSC) decoding algorithm, a decoding algorithm (CSS-SSR-Flip) based on critical simplified set (CSS) and simplified sequence repetition (SSR) nodes was designed. Firstly, the information bit of the longest repetition (REP) node in SSR was selected as candidate bit (CB), thus constructing a CSS based on SSR. Corresponding flip metrics and flip criterion were designed according to the decoding characteristics of SSR nodes. Secondly, the CB reliability was measured by considering the influence of repetition sequences and the source of SSR nodes on decoding, and suboptimal repetition sequences were selected to complete SSR node flip operations during specific CB flips. Experimental data shows that at frame error rates of <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/21552BC7-E00E-4802-B7F8-045B98659DAF-M002.jpg"><?fx-imagestate width="5.41866684" height="2.53999996"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/21552BC7-E00E-4802-B7F8-045B98659DAF-M002c.jpg"><?fx-imagestate width="5.41866684" height="2.53999996"?></graphic></alternatives></inline-formula>, CSS-SSR-Flip decoding algorithm is able to obtain more than 0.1 dB performance gain compared to the traditional fast simplified successive cancellation filp (Fast-SSC-Flip) decoding algorithm, and has the same decoding performance as the new Fast-SSC-Flip (New-Fast-SSC-Flip) decoding algorithm. However, compared to the traditional flip set size <italic>K</italic>, the CSS size of the proposed algorithm is reduced by up to 79.5%, and compared to the critical set (CS), the set size can be reduced by up to 23.1%.