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International SoC Design Conference

Efficient Partial Sum Architecture and Memory Reduction Method for SC-Flip Polar Decoder

Jae Hong Roh, Useok Lee, Yongje Lee, Myung Hoon Sunwoo

Published Oct 6, 2021• 0 citations
Publisher

Abstract

To improve the error correction performance of successive cancellation (SC) decoding of polar codes, SC-flip (SCF) decoding was proposed. However, it requires large additional memory to save the decoding history for hardware implementation. This paper proposes a partial sum (PS) memory reduction method and a PS architecture for SCF decoders. We analyze the fractal structure of the generator matrix and propose a logic circuit to decide the corresponding row of the generator matrix for an arbitrary bit-index. The proposed design was implemented on the Xilinx Virtex-7 FPGA, which can reduce the number of flip-flops by up to 47% and the PS history memory size by 94% compared to other PS architectures.

DOI
10.1109/isocc53507.2021.9613860

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To improve the error correction performance of successive cancellation (SC) decoding of polar codes, SC-flip (SCF) decoding was proposed. However, it requires large additional memory to save the decoding history for hardware implementation. This paper proposes a partial sum (PS) memory reduction method and a PS architecture for SCF decoders. We analyze the fractal structure of the generator matrix and propose a logic circuit to decide the corresponding row of the generator matrix for an arbitrary bit-index. The proposed design was implemented on the Xilinx Virtex-7 FPGA, which can reduce the number of flip-flops by up to 47% and the PS history memory size by 94% compared to other PS architectures.
Although the successive cancelation (SC) algorithm works well for very long polar codes, its error performance for shorter polar codes is much worse. Several SC based list decoding algorithms have been proposed to improve the error performances of both long and short polar codes. A significant step of SC based list decoding algorithms is the updating of partial sums for all decoding paths. In this paper, we first proposed a lazy copy partial sum computation algorithm for SC based list decoding algorithms. Instead of copying partial sums directly, our lazy copy algorithm copies indices of partial sums. Based on our lazy copy algorithm, we propose a hybrid partial sum computation unit architecture, which employs both registers and memories so that the overall area efficiency is improved. Compared with a recent partial sum computation unit for list decoders, when the list size L = 4, our partial sum computation unit achieves an area saving of 23% and 63% for block length 213and 215, respectively.
Polar codes are a class of error-correcting codes that provably achieve the capacity of practical channels. The successive-cancellation flip (SCF) decoder is a low-complexity decoder that was proposed to improve the performance of the successive-cancellation (SC) decoder as an alternative to the high-complexity successive-cancellation list (SCL) decoder. The SCF decoder improves the error-correction performance of the SC decoder, but the variable execution time and the high worst-case execution time pose a challenge for the realization of receivers with fixed-time algorithms. The dynamic SCF (DSCF) variation of the SCF decoder further improves the error-correction performance but the challenge of decoding delay remains. In this work, we propose a simplified restart mechanism (SRM) that reduces the execution time of SCF and DSCF decoders through conditional restart of the additional trials from the second half of the codeword. We show that the proposed mechanism is able to improve the execution time characteristics of SCF and DSCF decoders while providing identical error-correction performance. For a DSCF decoder that can flip up to 3 simultaneous bits per decoding trial, the average execution time, the average additional execution time and the execution-time variance are reduced by approximately 31%, 37% and 57%, respectively. For this setup, the mechanism requires approximately 3.9% additional memory.
By adopting successive cancellation list decoding (SCL), polar codes demonstrate competitive error correction performance over LDPC and Turbo codes. However, SCL decoding suffers from high computational complexity and long decoding latency, especially when the list size is very large. Successive cancellation flip (SCF), as another decoding algorithm that can achieve high error correction performance, has a complexity that is close to that of successive cancellation (SC) decoding. With the observation that SCL and SCF decoding are similar at giving more chances to inspect possible codewords simultaneously or sequentially, a novel hybrid decoder is proposed in this paper, which essentially combines the ideas of SCF and SCL decoders. Moreover, in order to compensate for the degradation of performance caused by the reduction of path splitting and further reduce the decoding latency, the convolutional polar codes are adopted with a designed bit-flipping set. Simulation results demonstrate that the proposed decoder achieves the reduction of decoding latency while attaining better performance than conventional CRC-aided SCL decoder.
In order to achieve a magnificent error-correcting performance Successive Cancellation List (SCL) decoding is a powerful and excellent method which considers L decoding paths at each decoding stage concurrently. However, the conventional SCL decoder uses L copies of Successive Cancellation (SC) decoder for a list size of L thereby resulting in a massive increase in the hardware as the list size increases which is one of the major drawbacks of SCL decoder. One more drawback of SCL decoder architecture is the long latency of the architecture. Using the proposed efficient utilization of existing hardware architecture, there is a reduction in the number of Merged Processing Elements (MPE) by 39% for a list size of 2 and 45% for a list size of 4 when compared to the existing architectures and a vast reduction compared to conventional SCL decoder. The partial pipelining considered in this work can reduce the latency compared to conventional SCL multi-bit architecture to a greater extent.
Polar codes attract more and more attention of researchers in recent years, since its capacity achieving property. However, their error-correction performance under successive cancellation (SC) decoding is inferior to other modern channel codes at short or moderate blocklengths. SC-Flip (SCF) decoding algorithm shows higher performance than SC decoding by identifying possibly erroneous decisions made in initial SC decoding and flipping them in the sequential decoding attempts. However, it performs not well when there are more than one erroneous decisions in a codeword. In this paper, we propose a path metric aided bit-flipping decoding algorithm to identify and correct more errors efficiently. In this algorithm, the bit-flipping list is generated based on both log likelihood ratio (LLR) based path metric and bit-flipping metric. The path metric is used to verify the effectiveness of bit-flipping. In order to reduce the decoding latency and computational complexity, its corresponding pipeline architecture is designed. By applying these decoding algorithm and pipeline architecture, an improvement on error-correction performance can be got up to 0.25dB compared with SCF decoding at frame error rate of 10-4, with low average decoding latency.
Polar codes are a family of error correcting codes that achieves the symmetric capacity of memoryless channels when the code length N tends to infinity. However, moderate code lengths are required in most of wireless digital applications to limit the decoding latency. In some other applications, such as optical communications or quantum key distribution, the latency introduced by very long codes is not an issue. The main challenge is to design codes with the best error correction capability, a tractable complexity and a high throughput. In such a context, SC decoding is an interesting solution because its performance improves with N while the computational complexity scales almost linearly. In this paper, we propose to improve the scalability of SC decoders thanks to four architectural optimizations. The resulting SC decoder is implemented on an FPGA device and favorably compares with state-of-the-art scalable SC decoders. Moreover, a 222polar code SC decoder is implemented on a Stratix-5 FPGA. This code length is twice larger than the ones achieved in previous works. To the best of our knowledge, this is the first architecture for which a N = 4 million bits polar code can be actually decoded on a reconfigurable circuit.