In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-froze...In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-frozen symbols exist,where the frozen bits in these symbols can be used as activecheck bits to facilitate the decoder.The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes,admitting an easily configurable and flexible implementation,which is an obvious advantage over the existing nonbinary polar codes based on ReedSolomon(RS)codes.A low-complexity decoding method is also introduced,in which only more competitive symbols are considered rather than the whole q symbols in the finite field.To support high spectral efficiency,we also present,in addition to the single level coded modulation scheme with field-matched modulation order,a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity.Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency,suggesting a potential application for future ultra-reliable and low-latency communications(URLLC).展开更多
<div style="text-align:justify;"> Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm im...<div style="text-align:justify;"> Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree. </div>展开更多
<div style="text-align:justify;"> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">This artic...<div style="text-align:justify;"> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's </span><span><a href="http://publicationethics.org/files/retraction%20guidelines.pdf"><span style="font-size:10.0pt;font-family:;" "="">Retraction Guidelines</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"="">. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.</span><span style="font-size:10.0pt;font-family:" color:black;"=""></span> </p> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">Please see the </span><span><a href="https://www.scirp.org/journal/paperinformation.aspx?paperid=101825"><span style="font-size:10.0pt;font-family:;" "="">article page</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> for more details. </span><span><a href="https://www.scirp.org/pdf/opj_2020072814494052.pdf"><span style="font-size:10.0pt;font-family:;" "="">The full retraction notice</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> in PDF is preceding the original paper which is marked "RETRACTED". </span> </p> <br /> </div>展开更多
基金supported in part by the National Key R&D Program of China(2021YFA1000500)by the National Natural Science Foundation of China(62171356).
文摘In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-frozen symbols exist,where the frozen bits in these symbols can be used as activecheck bits to facilitate the decoder.The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes,admitting an easily configurable and flexible implementation,which is an obvious advantage over the existing nonbinary polar codes based on ReedSolomon(RS)codes.A low-complexity decoding method is also introduced,in which only more competitive symbols are considered rather than the whole q symbols in the finite field.To support high spectral efficiency,we also present,in addition to the single level coded modulation scheme with field-matched modulation order,a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity.Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency,suggesting a potential application for future ultra-reliable and low-latency communications(URLLC).
文摘<div style="text-align:justify;"> Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree. </div>
文摘<div style="text-align:justify;"> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's </span><span><a href="http://publicationethics.org/files/retraction%20guidelines.pdf"><span style="font-size:10.0pt;font-family:;" "="">Retraction Guidelines</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"="">. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.</span><span style="font-size:10.0pt;font-family:" color:black;"=""></span> </p> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">Please see the </span><span><a href="https://www.scirp.org/journal/paperinformation.aspx?paperid=101825"><span style="font-size:10.0pt;font-family:;" "="">article page</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> for more details. </span><span><a href="https://www.scirp.org/pdf/opj_2020072814494052.pdf"><span style="font-size:10.0pt;font-family:;" "="">The full retraction notice</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> in PDF is preceding the original paper which is marked "RETRACTED". </span> </p> <br /> </div>
