Rate-Flexible Fast Polar Decoders

Polar codes have gained extensive attention during the past few years and recently they have been selected for the next generation of wireless communications standards (5G). Successive-cancellation-based (SC-based) decoders, such as SC list (SCL) and SC flip (SCF), provide a reasonable error performance for polar codes at the cost of low decoding speed. Fast SC-based decoders, such as Fast-SSC, Fast-SSCL, and Fast-SSCF, identify the special constituent codes in a polar code graph off-line, produce a list of operations, store the list in memory, and feed the list to the decoder to decode the constituent codes in order efficiently, thus increasing the decoding speed. However, the list of operations is dependent on the code rate and as the rate changes, a new list is produced, making fast SC-based decoders not rate-flexible. In this paper, we propose a completely rate-flexible fast SC-based decoder by creating the list of operations directly in hardware, with low implementation complexity. We further propose a hardware architecture implementing the proposed method and show that the area occupation of the rate-flexible fast SC-based decoder in this paper is only $38\%$ of the total area of the memory-based base-line decoder when 5G code rates are supported

On the Decoding of Polar Codes on Permuted Factor Graphs

Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications. However, the error-correction performance of polar codes under BP decoding is far from the requirements of 5G. It has been shown that the error-correction performance of BP can be improved if the decoding is performed on multiple permuted factor graphs of polar codes. However, a different BP decoding scheduling is required for each factor graph permutation which results in the design of a different decoder for each permutation. Moreover, the selection of the different factor graph permutations is at random, which prevents the decoder to achieve a desirable error-correction performance with a small number of permutations. In this paper, we first show that the permutations on the factor graph can be mapped into suitable permutations on the codeword positions. As a result, we can make use of a single decoder for all the permutations. In addition, we introduce a method to construct a set of predetermined permutations which can provide the correct codeword if the decoding fails on the original permutation. We show that for the 5G polar code of length $1024$, the error-correction performance of the proposed decoder is more than $0.25$ dB better than that of the BP decoder with the same number of random permutations at the frame error rate of $10^{-4}$

Comparison of Polar Decoders with Existing Low-Density Parity-Check and Turbo Decoders

Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of codes has not been thoroughly studied. Towards this end, in this paper, we perform a comparison of polar decoders against LDPC and Turbo decoders that are used in existing communications standards. More specifically, we compare both the error-correction performance and the hardware efficiency of the corresponding hardware implementations. This comparison enables us to identify applications where polar codes are superior to existing error-correction coding solutions as well as to determine the most promising research direction in terms of the hardware implementation of polar decoders.Comment: Fixes small mistakes from the paper to appear in the proceedings of IEEE WCNC 2017. Results were presented in the "Polar Coding in Wireless Communications: Theory and Implementation" Worksho

Improved Successive Cancellation Flip Decoding of Polar Codes Based on Error Distribution

Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar codes has mediocre error-correction performance on short to moderate codeword lengths: the SC-Flip decoding algorithm is one of the solutions that have been proposed to overcome this issue. On the other hand, SC-Flip has a higher implementation complexity compared to SC due to the required log-likelihood ratio (LLR) selection and sorting process. Moreover, it requires a high number of iterations to reach good error-correction performance. In this work, we propose two techniques to improve the SC-Flip decoding algorithm for low-rate codes, based on the observation of channel-induced error distributions. The first one is a fixed index selection (FIS) scheme to avoid the substantial implementation cost of LLR selection and sorting with no cost on error-correction performance. The second is an enhanced index selection (EIS) criterion to improve the error-correction performance of SC-Flip decoding. A reduction of $24.6\%$ in the implementation cost of logic elements is estimated with the FIS approach, while simulation results show that EIS leads to an improvement on error-correction performance improvement up to $0.42$ dB at a target FER of $10^{-4}$.Comment: This version of the manuscript corrects an error in the previous ArXiv version, as well as the published version in IEEE Xplore under the same title, which has the DOI:10.1109/WCNCW.2018.8368991. The corrections include all the simulations of SC-Flip-based and SC-Oracle decoders, along with associated comments in-tex