Enhanced Loop-weakened Belief Propagation Algorithm for Performance Enhanced Polar Code Decoders

A polar code decoder based on the belief propagation algorithm is desirable because of the potentially low latency and its suitability for parallel execution on multicore and SIMD processors. However, current state-of-the-art algorithms require many iterations to achieve comparable bit and frame error rate compared to successive cancellation algorithms. Also, the current state-of-the-art belief propagation algorithms have a high computational complexity compared to successive cancellation. In this paper we present an enhanced belief propagation algorithm, in which parts of the computations are altered to reduce the negative effect of the short cycles in the polar code factor graph. Our proposed algorithm has a gain of approx+0.4mathbf{dB} in both frame and bit error rate compared to successive cancellation and a gain of approx+0.16mathbf{dB} and approx+0.13mathbf{dB} at a frame and bit error rate of 10-3 respectively, compared to belief propagation. Also, the maximum number of iterations of our algorithm is reduce to 0.6cdot I_{max}. As a result, the latency is up to approx 11 times lower compared to successive cancellation and up to approx 1.8 times lower compared to the current state-of-the-art belief propagation polar code algorithm. Furthermore, the reduction in the maximum iteration count results in a lower power consumption after implementation.</p

Computational Complexity Reduced Belief Propagation Algorithm for Polar Code Decoders

The belief propagation algorithm is desirable for a polar code based decoder, because of the potentially low latency and the ability of integration in digital signal processing units or other multi-core processor systems to parallelize the computations. Although belief propagation polar code decoder algorithms have the ability for a highly parallelized imple-mentation, the algorithms require many iterations to achieve a comparable frame error rate and bit error rate with respect to a successive cancellation polar code algorithm. The iterative nature of the belief propagation algorithms also result in a higher computational complexity, i.e. O(IN(2log_{2} N-1)) compared to the computational complexity O(Nlog_{2}N) of the successive cancellation decoder algorithm. In this paper we propose several simplifications for a simplified belief propagation algorithm for polar code decoders, where the arithmetic complexity of the nodes is reduced. The proposed belief propagation algorithm shows preliminary results of a net reduction of the arithmetic complexity of ≈ 13%. This reduction is a result of the reduced number of arithmetic operations, i.e., additions, compares, and multiplications, without a lost in error-correcting performance.</p

Software Implementation and Performance of a Computational Complexity Reduced Belief Propagation Polar Code Decoder

The belief propagation algorithm is one of the preferred algorithms for a polar code based decoder that can potentially achieve the lowest latency. Although belief propagation polar code algorithms have the ability for a highly parallelized implementation, they require more iterations to achieve a comparable frame error rate and bit error rate compared to the successive cancellation polar code algorithm. The iterative nature of the belief propagation algorithms also results in a higher computational complexity, i.e. O(N(2log2N-1)) compared to the computational complexity O(Nlog2N) of the successive cancellation decoder algorithm. In this paper we propose several software implementations of belief propagation polar code decoders using the computational complexity reduced belief propagation algorithm and the enhanced loop-weakened belief propagation algorithm, to increase the number of decoded codes per second. Compared to a baseline belief propagation implementation, our proposed radix-2 and radix-4 implementations increase the throughput by approximately 15.4% and 22.04% respectively. This gain is the result of a reduction of arithmetic operations, i.e., additions, compares, and multiplications, which is obtained without a loss in error-correcting performance.</p