Simplified Successive Cancellation List Decoding of PAC Codes

Polar codes are the first class of structured channel codes that achieve the symmetric capacity of binary channels with efficient encoding and decoding. In 2019, Arikan proposed a new polar coding scheme referred to as polarization-adjusted convolutional (PAC)} codes. In contrast to polar codes, PAC codes precode the information word using a convolutional code prior to polar encoding. This results in material coding gain over polar code under Fano sequential decoding as well as successive cancellation list (SCL) decoding. Given the advantages of SCL decoding over Fano decoding in certain scenarios such as low-SNR regime or where a constraint on the worst case decoding latency exists, in this paper, we focus on SCL decoding and present a simplified SCL (SSCL) decoding algorithm for PAC codes. SSCL decoding of PAC codes reduces the decoding latency by identifying special nodes in the decoding tree and processing them at the intermediate stages of the graph. Our simulation results show that the performance of PAC codes under SSCL decoding is almost similar to the SCL decoding while having lower decoding latency.Comment: 7 pages, 3 figure

List Decoding of Arikan's PAC Codes

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short block lengths is far from optimal. Arikan has recently presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. Such PAC codes provide dramatic improvement in performance as compared to both standard successive-cancellation decoding as well as CRC-aided list decoding. Arikan's PAC codes are based primarily upon the following ideas: replacing CRC precoding with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. His simulations show that PAC codes, resulting from the combination of these ideas, are close to finite-length bounds on the performance of any code under ML decoding. One of our main goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size $L$ is moderately large (say, $L \ge 128$). List decoding has distinct advantages over sequential decoding is certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, using these estimates to approximate the union bound on their performance under ML decoding. These results indicate that PAC codes are superior to both polar codes and Reed-Muller codes, and suggest that the goal of rate-profiling may be to optimize the weight distribution at low weights.Comment: 9 pages, 10 figures, abridged version of this paper will be presented at the International Symposium on Information Theory, June 202

A Randomized Construction of Polar Subcodes

A method for construction of polar subcodes is presented, which aims on minimization of the number of low-weight codewords in the obtained codes, as well as on improved performance under list or sequential decoding. Simulation results are provided, which show that the obtained codes outperform LDPC and turbo codes.Comment: Accepted to ISIT 2017 Formatting change

Learning to Construct Nested Polar Codes: An Attention-Based Set-to-Element Model

As capacity-achieving codes under successive cancellation (SC) decoding, nested polar codes have been adopted in 5G enhanced mobile broadband. To optimize the performance of the code construction under practical decoding, e.g. SC list (SCL) decoding, artificial intelligence based methods have been explored in the literature. However, the structure of nested polar codes has not been fully exploited for code construction. To address this issue, this letter transforms the original combinatorial optimization problem for the construction of nested polar codes into a policy optimization problem for sequential decision, and proposes an attention-based set-to-element model, which incorporates the nested structure into the policy design. Based on the proposed architecture for the policy, a gradient based algorithm for code construction and a divide-and-conquer strategy for parallel implementation are further developed. Simulation results demonstrate that the proposed construction outperforms the state-of-the-art nested polar codes for SCL decoding