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

Pipelined Architecture for Soft-decision Iterative Projection Aggregation Decoding for RM Codes

The recently proposed recursive projection-aggregation (RPA) decoding algorithm for Reed-Muller codes has received significant attention as it provides near-ML decoding performance at reasonable complexity for short codes. However, its complicated structure makes it unsuitable for hardware implementation. Iterative projection-aggregation (IPA) decoding is a modified version of RPA decoding that simplifies the hardware implementation. In this work, we present a flexible hardware architecture for the IPA decoder that can be configured from fully-sequential to fully-parallel, thus making it suitable for a wide range of applications with different constraints and resource budgets. Our simulation and implementation results show that the IPA decoder has 41% lower area consumption, 44% lower latency, four times higher throughput, but currently seven times higher power consumption for a code with block length of 128 and information length of 29 compared to a state-of-the-art polar successive cancellation list (SCL) decoder with comparable decoding performance

Partial Sums Generation Architecture for Successive Cancellation Decoding of Polar Codes

Polar codes are a new family of error correction codes for which efficient hardware architectures have to be defined for the encoder and the decoder. Polar codes are decoded using the successive cancellation decoding algorithm that includes partial sums computations. We take advantage of the recursive structure of polar codes to introduce an efficient partial sums computation unit that can also implements the encoder. The proposed architecture is synthesized for several codelengths in 65nm ASIC technology. The area of the resulting design is reduced up to 26% and the maximum working frequency is improved by ~25%.Comment: Submitted to IEEE Workshop on Signal Processing Systems (SiPS)(26 April 2012). Accepted (28 June 2013