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arXiv:1411.7282 · Asilomar Conference on Signals, Systems and Computers (ACSSC)

Successive cancellation list polar decoder using log-likelihood ratios

Bo Yuan, Keshab K. Parhi

Published Nov 1, 2014• 42 citations
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Abstract

Successive cancellation list (SCL) decoding algorithm is a powerful method that can help polar codes achieve excellent error-correcting performance. However, the current SCL algorithm and decoders are based on likelihood or log-likelihood forms, which render high hardware complexity. In this paper, we propose a log-likelihood-ratio (LLR)-based SCL (LLR-SCL) decoding algorithm, which only needs half the computation and storage complexity than the conventional one. Then, based on the proposed algorithm, we develop low-complexity VLSI architectures for LLR-SCL decoders. Analysis results show that the proposed LLR-SCL decoder achieves 50% reduction in hardware and 98% improvement in hardware efficiency.

DOI
10.1109/acssc.2014.7094505

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Successive cancellation list (SCL) decoding algorithm is a powerful method that can help polar codes achieve excellent error-correcting performance. However, the current SCL algorithm and decoders are based on likelihood or log-likelihood forms, which render high hardware complexity. In this paper, we propose a log-likelihood-ratio (LLR)-based SCL (LLR-SCL) decoding algorithm, which only needs half the computation and storage complexity than the conventional one. Then, based on the proposed algorithm, we develop low-complexity VLSI architectures for LLR-SCL decoders. Analysis results show that the proposed LLR-SCL decoder achieves 50% reduction in hardware and 98% improvement in hardware efficiency.
Successive cancellation list (SCL) decoding algorithm for polar codes is one of the best decoding algorithms due to its excellent decoding performance. The decoding complexity of conventional SCL decoding algorithm is O(LN log N). The decoding complexity will increase as the size of the list increases. To solve this problem, we introduce an improved SCL decoding algorithm based on the sequential probability ratio test (SPRT). The proposed algorithm use double thresholds to decode the polar codes instead of single threshold decision used by the conventional SCL algorithm. Numerical results have shown that for (1024, 512) polar code, the proposed SPRT-SCL decoder can achieve a reduction in decoding complexity, and keep the similar decoding performance compared with conventional SCL decoder.
We present an LLR-based implementation of the successive cancellation list (SCL) decoder. To this end, we associate each decoding path with a metric which (i) is a monotone function of the path's likelihood and (ii) can be computed efficiently from the channel LLRs. The LLR-based formulation leads to a more efficient hardware implementation of the decoder compared to the known log-likelihood based implementation. Synthesis results for an SCL decoder with block-length of N = 1024 and list sizes of L = 2 and L = 4 confirm that the LLR-based decoder has considerable area and operating frequency advantages in the orders of 50% and 30%, respectively.
We show that successive cancellation list decoding can be formulated exclusively using log-likelihood ratios. In addition to numerical stability, the log-likelihood ratio based formulation has useful properties that simplify the sorting step involved in successive cancellation list decoding. We propose a hardware architecture of the successive cancellation list decoder in the log-likelihood ratio domain which, compared with a log-likelihood domain implementation, requires less irregular and smaller memories. This simplification, together with the gains in the metric sorter, lead to$ 56\%$to137%137\%137%higher throughput per unit area than other recently proposed architectures. We then evaluate the empirical performance of the CRC-aided successive cancellation list decoder at different list sizes using different CRCs and conclude that it is important to adapt the CRC length to the list size in order to achieve the best error-rate performance of concatenated polar codes. Finally, we synthesize conventional successive cancellation decoders at large block-lengths with the same block-error probability as our proposed CRC-aided successive cancellation list decoders to demonstrate that, while our decoders have slightly lower throughput and larger area, they have a significantly smaller decoding latency.
Successive cancellation list (SCL) decoding for polar codes has the ability to achieve Shannon capacity over the binary discrete memoryless channel. However, a large list size is required to achieve the Shannon capacity limit. Consequently, this paper proposes a novel iterative method for the CA-SCL decoder based on frozen bits to improve the error-correction performance of CA-SCL decoding for polar codes with smaller list sizes. The proposed technique determines the vulnerable channel log-likelihood ratios (LLRs) for frozen bits that degrade the CA-SCL decoding error correction performance and corrects them for the next CA-SCL decoding attempt. We analyze the behavior of wrongly estimated LLRs of frozen bits during CA-SCL decoding and design an attenuation factor set using a greedy algorithm. The proposed technique employs iterative CA-SCL decoding and revises the wrongly estimated frozen bit LLRs using the attenuation factor set during the decoding process. The simulation results show that the proposed technique achieves a block error rate (BLER) performance gain of up to 0.25 compared with the CA-SCL decoder, with a minor increase in computational complexity. Moreover, the attenuation factor set can be adjusted arbitrarily to balance performance and complexity.
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.
The soft-output successive cancellation list (SO-SCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder for polar codes. However, the sequential nature of SCL decoding leads to a high decoding latency for the SO-SCL decoder. In this paper, we propose a soft-output fast SCL (SO-FSCL) decoder by incorporating node-based fast decoding into the SO-SCL framework. Simulation results demonstrate that the proposed SO-FSCL decoder significantly reduces the decoding latency without loss of performance compared with the SO-SCL decoder.