We consider practical hardware implementation of Polar decoders. To reduce latency due to the serial nature of successive cancellation (SC), existing optimizations improve parallelism with two approaches, i.e., multi-bit decision or reduced path splitting. In this paper, we combine the two procedures into one with an error-pattern-based architecture. It simultaneously generates a set of candidate paths for multiple bits with pre-stored patterns. For rate-1 (R1) or single parity-check (SPC) nodes, we prove that a small number of deterministic patterns are required to guarantee performance preservation. For general nodes, low-weight error patterns are indexed by syndrome in a look-up table and retrieved in O(1) time. The proposed flip-syndrome-list (FSL) decoder fully parallelizes all constituent code blocks without sacrificing performance, thus is suitable for ultra-low-latency applications. Meanwhile, two code construction optimizations are presented to further reduce complexity and improve performance, respectively.
Polar codes @cite_8 @cite_16 have been selected for the fifth generation (5G) wireless standard. With state-of-the-art code construction techniques @cite_19 @cite_0 @cite_5 and SC-List (SCL) decoding algorithm @cite_10 @cite_9 @cite_11 @cite_12 @cite_1 @cite_14 @cite_3 @cite_7 , Polar codes demonstrate competitive performance over LDPC and Turbo codes in terms of block error rate (BLER). Beyond 5G, ultra-low decoding latency emerges as a key requirement for applications such as autonomous driving and virtual reality. The latency of practical Polar decoders, e.g., an SC-list decoder with list size @math , is relatively long due to the serial processing nature.
@cite_14 @cite_7 @cite_8 @cite_9 @cite_1 @cite_3 @cite_0 @cite_19 @cite_5 @cite_16 @cite_10 @cite_12 @cite_11
2240900403 2003204237 2228116382 2950110977 2106045225 2101207956 2601496744
Polar codes, as the first provable capacity-achieving error-correcting codes, have received much attention in recent years. However, the decoding performance of polar codes with traditional successive-cancellation (SC) algorithm cannot match that of the low-density parity-check or Turbo codes. Because SC list (SCL) decoding algorithm can significantly improve the error-correcting performance of polar codes, design of SCL decoders is important for polar codes to be deployed in practical applications. However, because the prior latency reduction approaches for SC decoders are not applicable for SCL decoders, these list decoders suffer from the long-latency bottleneck. In this paper, we propose a multibit-decision approach that can significantly reduce latency of SCL decoders. First, we present a reformulated SCL algorithm that can perform intermediate decoding of 2 b together. The proposed approach, referred as 2-bit reformulated SCL ( 2b-rSCL ) algorithm , can reduce the latency of SCL decoder from ( @math ) to ( @math ) clock cycles without any performance loss. Then, we extend the idea of 2-b-decision to general case, and propose a general decoding scheme that can perform intermediate decoding of any @math bits simultaneously. This general approach, referred as @math -bit reformulated SCL ( @math b-rSCL ) algorithm , can reduce the overall decoding latency to as short as @math cycles. Furthermore, on the basis of the proposed algorithms, very large-scale integration architectures for 2b-rSCL and 4b-rSCL decoders are synthesized. Compared with a prior SCL decoder, the proposed (1024, 512) 2b-rSCL and 4b-rSCL decoders can achieve 21 and 60 reduction in latency, 1.66 and 2.77 times increase in coded throughput with list size 2, and 2.11 and 3.23 times increase in coded throughput with list size 4, respectively. This paper investigates block error rate (BLER) performance and computational complexity of candidate channel coding schemes for ultra-reliable low latency communication (URLLC) in 5G. The considered candidates are the same as those identified in 3GPP: turbo, LDPC, polar, and convolutional codes. Details of code constructions and decoding algorithms are provided with computational complexity analysis. Code construction parameters, number of iterations, and list sizes are selected to provide a fair comparison among candidate coding schemes. Simulation results on BLER are shown for several code rates and small-to-moderate block sizes. The results reveal that polar and LDPC codes outperform turbo codes for short block sizes of 40 bits, while the opposite is true for medium block sizes of 200 bits. None of the schemes is a clear winner at all considered block sizes and coding rates. Other aspects like implementation complexity, latency, and flexibility will also be important when deciding the URLLC coding scheme. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 .