# Improvement of Fast Simplified Successive-Cancellation Decoder for Polar Codes
## 1 Introduction  
Polar codes [1] have been proven to achieve the symmetric capacity of memoryless channels with a successive-cancellation (SC) decoder. They have low implementation complexity and a very low error-floor [2]. However, the SC decoding speed is limited by the serial process, resulting in a high decoding latency. To decode a length-\(N\) polar code, the basic SC decoder should require \(2(N-1)\) clock cycles [3]. In [4], a simplified SC (SSC) decoder is reported, for which the latency is reduced by classifying three types of constituent code nodes in the decoding tree. These are rate-zero (R-0), rate-one (R-1), and rate-other (R-other) nodes, the leaves of which are all frozen bits, all information bits, and partially frozen and information bits, respectively. The local decoder of an R-1 node uses threshold detection. Further, an R-0 node is a zero vector at any time. An R-other node retains the SC decoding rules and contributes the most latency. Two methods to improve the parallelism of the R-other node have been developed: the recognition-based method [5; 6; 7; 8] and the check-based method [9; 10; 11]. The recognition-based method recognizes the constituent codes offline before decoding. The Fast Simplified SC (Fast-SSC) decoder has been introduced [5] to recognize the two other constituent codetypes (apart from R-0, R-1, and R-other); thus, the repetition (Rep) codes and single parity-check (SPC) codes can be decoded in parallel with low-complexity algorithms without traversing their corresponding sub-trees. Both the SSC decoder and Fast-SSC decoder provide significant latency reduction in comparison with that obtained from the SC decoder, while exhibiting the same performance as the SC decoder [5]. Further, some software decoders explore the implementation of the Fast-SSC algorithm [6; 7; 8]. However, the decoding latencies of the SSC and Fast-SSC decoders are constant without the influence of the channel condition. The check-based method is designed to convert the R-other nodes to the constituent codes online, when a specific condition or check is satisfied [9; 10; 11]. To decrease the latency, resource constrained maximum-likelihood (ML) decoding on R-other nodes has been proposed [9]. To obtain the Improved Modified SC(IMSC) Decoder, the frozen-bit check (FC) has been applied to the SSC decoder [10] (Note that a similar method has been studied in [11]). Assuming that an R-other node follows the R-1 node rule of the SSC decoder, the bit estimates of the current code and its leaf node are decoded directly. If the bit estimates of all frozen leaf nodes are zero following checking, the FC condition is satisfied. Then, the bit estimate of the R-other node obtained in the previous step is valid, and there is no need to traverse the corresponding sub-trees. Otherwise, the R-other node still follows the original SC decoding rules. With this method, latency and complexity are reduced without loss of error-correction performance [10]. Note that the percentage of R-other nodes satisfying the FC condition increases with the signal-to-noise ratio (SNR), which introduces dynamic features in the decoding process. However, the decoding latency of the high-rate IMSC decoder is extremely high in the low-SNR range. In this study, we propose a new type of latency reduction method called the Fast-ISSC algorithm, which performs the FC on the R-other nodes of the Fast-SSC pruning tree. Before decoding, the decoding tree becomes a Fast-SSC pruning tree through the recognition-based method. During decoding, the specific constituent codes follow the specific decoding rules. The R-other nodes are converted to R-1 nodes when the FC condition is satisfied. The Fast-ISSC decoder integrates the Fast-SSC algorithm and the FC method. The relationships between the various SC decoding latency reduction methods are shown in Figure 1.  
The proposed Fast-ISSC algorithm is the first technique that integrates the stability of the recognition-based method and the dynamics of the check-based method.