arXiv subjects

Jiajie Tong

Publications and source records attributed to Jiajie Tong.

13 recordsLinked to original sources

arXiv2026

A Path-Survival Analytical Framework for SCL Decoding of Polar Codes

A theoretical analysis of CRC-aided successive cancellation list (CA-SCL) decoding for polar codes remains an open problem, despite its widespread practical adoption. While low-density parity-check (LDPC) codes benefit from mature analytical tools, such as density evolution (DE), for predicting the performance of belief-propagation (BP) decoding, similar techniques are not directly applicable to CA-SCL decoding. This limitation stems from the complex path-pruning mechanism inherent in CA-SCL decoding. In this paper, we propose an analytical framework based on a novel path-survival model that captures the evolution of the correct path's rank during decoding. The proposed framework enables efficient prediction of CA-SCL decoding performance without requiring exhaustive list-specific Monte Carlo simulations. Extensive numerical evaluations demonstrate its effectiveness across a wide range of code lengths, code rates, list sizes, and channel models.

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arXiv2026

Beyond 1$\to$N Decoding: Capacity-Aware Rateless Polar Codes for IR-HARQ

This paper introduces a novel framework for polar codes, designed for flexible Incremental Redundancy Hybrid Automatic Repeat Request (IR-HARQ). By generalizing the decoding order beyond the standard 1$\to$N sequence, we enable a capacity-aware scheduling strategy that prioritizes the decoding of reliable subblocks. The framework integrates nested parity-check polar construction and reverse bit-mapping to support continuous and arbitrary transmission lengths $E \in [N_{\min}, N_{\max}]$. Simulation results show that the proposed rateless codes match the coding gain of independently optimized fixed-rate codes across the entire range of rates and lengths. With a validated hardware implementation, this work provides a practical solution for next-generation wireless data channels.

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arXiv2024

Adaptive Perturbation Enhanced SCL Decoder for Polar Codes

For polar codes, successive cancellation list (SCL) decoding algorithm significantly improves finite-length performance compared to SC decoding. SCL-flip decoding can further enhance the performance but the gain diminishes as code length increases, due to the difficulty in locating the first error bit position. In this work, we introduce an SCL-perturbation decoding algorithm to address this issue. A basic version of the algorithm introduces small random perturbations to the received symbols before each SCL decoding attempt, and exhibits non-diminishing gain at large block lengths. Its enhanced version adaptively performs random perturbations or directional perturbation on each received symbol according to previous decoding results, and managed to correct more errors with fewer decoding attempts. Extensive simulation results demonstrate stable gains across various code rates, lengths and list sizes. To the best of our knowledge, this is the first SCL enhancement with non-diminishing gains as code length increases, and achieves unprecedented efficiency. With only one additional SCL-$L$ decoding attempt (in total two), the proposed algorithm achieves SCL-$2L$-equivalent performance. Since the gain is obtained without increasing list size, the algorithm is best suited for hardware implementation.

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arXiv2023

On the Message Passing Efficiency of Polar and Low-Density Parity-Check Decoders

This study focuses on the efficiency of message-passing-based decoding algorithms for polar and low-density parity-check (LDPC) codes. Both successive cancellation (SC) and belief propagation (BP) decoding algorithms are studied {in} the message-passing framework. Counter-intuitively, SC decoding demonstrates the highest decoding efficiency, although it was considered a weak decoder {in terms of} error-correction performance. We analyze the complexity-performance tradeoff to dynamically track the decoding efficiency, where the complexity is measured by the number of messages passed (NMP), and the performance is measured by the statistical distance to the maximum a posteriori (MAP) estimate. This study offers a new insight into the contribution of each message passed in decoding, and compares various decoding algorithms on a message-by-message level. The analysis corroborates recent results on terabits-per-second polar SC decoders, and might shed light on better scheduling strategies.

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arXiv2021

Fast polar codes for terabits-per-second throughput communications

Targeting high-throughput and low-power communications, we implement two successive cancellation (SC) decoders for polar codes. With $16nm$ ASIC technology, the area efficiency and energy efficiency are $4Tbps/mm^2$ and $0.63pJ/bit$, respectively, for the unrolled decoder, and $561Gbps/mm^2$ and $1.21pJ/bit$, respectively, for the recursive decoder. To achieve such a high throughput, a novel code construction, coined as fast polar codes, is proposed and jointly optimized with a highly-parallel SC decoding architecture. First, we reuse existing modules to fast decode more outer code blocks, and then modify code construction to facilitate faster decoding for all outer code blocks up to a degree of parallelism of $16$. Furthermore, parallel comparison circuits and bit quantization schemes are customized for hardware implementation. Collectively, they contribute to an $2.66\times$ area efficiency improvement and $33\%$ energy saving over the state of the art.

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arXiv2021

A unified polar decoder platform for low-power and low-cost devices

In this paper, we design a polar decoding platform for diverse application scenarios that require low-cost and low-power communications. Specifically, prevalent polar decoders such as successive cancellation (SC), SC-list (SCL) and Fano decoders are all supported under the same architecture. Unlike high-throughput or low-latency decoders that promote parallelism, this architecture promotes serialization by repeatedly calling a ``sub-process'' that is executed by a core module. The resulting serial SCL-8 decoder is only 3 times as big as an SC decoder. Cost and power are minimized through resource sharing and adaptive decoding techniques, etc. We carried out performance simulation and hardware implementation to evaluate the actual chip area and energy consumption.

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arXiv2020

A Soft Cancellation Decoder for Parity-Check Polar Codes

Polar codes has been selected as the channel coding scheme for 5G new radio (NR) control channel. Specifically, a special type of parity-check polar (PC-Polar) codes was adopted in uplink control information (UCI). In this paper, we propose a parity-check soft-cancellation (PC-SCAN) algorithm and its simplified version to decode PC-Polar codes. The potential benefits are two-fold. First, PC-SCAN can provide soft output for PC-Polar codes, which is essential for advanced turbo receivers. Second, the decoding performance is better than that of successive cancellation (SC). This is due to the fact that parity-check constraints can be exploited by PC-SCAN to enhance the reliability of other information bits over the iterations. Moreover, we describe a cyclic-shift-register (CSR) based implementation "CSR-SCAN" to reduce both hardware cost and latency with minimum performance loss.

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arXiv2020

Toward Terabits-per-second Communications: A High-Throughput Hardware Implementation of $G_N$-Coset Codes

Recently, a parallel decoding algorithm of $G_N$-coset codes was proposed.The algorithm exploits two equivalent decoding graphs.For each graph, the inner code part, which consists of independent component codes, is decoded in parallel. The extrinsic information of the code bits is obtained and iteratively exchanged between the graphs until convergence. This algorithm enjoys a higher decoding parallelism than the previous successive cancellation algorithms, due to the avoidance of serial outer code processing. In this work, we present a hardware implementation of the parallel decoding algorithm, it can support maximum $N=16384$. We complete the decoder's physical layout in TSMC $16nm$ process and the size is $999.936μm\times 999.936μm, \,\approx 1.00mm^2$. The decoder's area efficiency and power consumption are evaluated for the cases of $N=16384,K=13225$ and $N=16384, K=14161$. Scaled to $7nm$ process, the decoder's throughput is higher than $477Gbps/mm^2$ and $533Gbps/mm^2$ with five iterations.

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arXiv2020

Toward Terabits-per-second Communications: Low-Complexity Parallel Decoding of $G_N$-Coset Codes

Recently, a parallel decoding framework of $G_N$-coset codes was proposed. High throughput is achieved by decoding the independent component polar codes in parallel. Various algorithms can be employed to decode these component codes, enabling a flexible throughput-performance tradeoff. In this work, we adopt SC as the component decoders to achieve the highest-throughput end of the tradeoff. The benefits over soft-output component decoders are reduced complexity and simpler (binary) interconnections among component decoders. To reduce performance degradation, we integrate an error detector and a log-likelihood ratio (LLR) generator into each component decoder. The LLR generator, specifically the damping factors therein, is designed by a genetic algorithm. This low-complexity design can achieve an area efficiency of $533Gbps/mm^2$ under 7nm technology.

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arXiv2019

On the Construction of $G_N$-coset Codes for Parallel Decoding

In this paper, we propose a type of $G_N$-coset codes for a highly parallel stage-permuted turbo-like decoder. The decoder exploits the equivalence between two stage-permuted factor graphs of $G_N$-coset codes. Specifically, the inner codes of a $G_N$-coset code consist of independent component codes, thus are decoded in parallel. The extrinsic information of the code bits is obtained and iteratively exchanged between the two graphs until convergence. Accordingly, we explore a heuristic and flexible code construction method (information set selection) for various information lengths and coding rates. Simulations show that the proposed $G_N$-coset codes could achieve a coding performance comparable with polar codes but enjoy higher decoding parallelism.

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arXiv2019

An Asymmetric Adaptive SCL Decoder Hardware for Ultra-Low-Error-Rate Polar Codes

In theory, Polar codes do not exhibit an error floor under successive-cancellation (SC) decoding. In practice, frame error rate (FER) down to $10^{-12}$ has not been reported with a real SC list (SCL) decoder hardware. This paper presents an asymmetric adaptive SCL (A2SCL) decoder, implemented in real hardware, for high-throughput and ultra-reliable communications. We propose to concatenate multiple SC decoders with an SCL decoder, in which the numbers of SC/SCL decoders are balanced with respect to their area and latency. In addition, a novel unequal-quantization technique is adopted. The two optimizations are crucial for improving SCL throughput within limited chip area. As an application, we build a link-level FPGA emulation platform to measure ultra-low FERs of 3GPP NR Polar codes (with parity-check and CRC bits). It is flexible to support all list sizes up to $8$, code lengths up to $1024$ and arbitrary code rates. With the proposed hardware, decoding speed is 7000 times faster than a CPU core. For the first time, FER as low as $10^{-12}$ is measured and quantization effect is analyzed.

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arXiv2018

A Flip-Syndrome-List Polar Decoder Architecture for Ultra-Low-Latency Communications

We consider practical hardware implementation of Polar decoders. To reduce latency due to the serial nature of successive cancellation (SC), existing optimizations improve parallelism with two approaches, i.e., multi-bit decision or reduced path splitting. In this paper, we combine the two procedures into one with an error-pattern-based architecture. It simultaneously generates a set of candidate paths for multiple bits with pre-stored patterns. For rate-1 (R1) or single parity-check (SPC) nodes, we prove that a small number of deterministic patterns are required to guarantee performance preservation. For general nodes, low-weight error patterns are indexed by syndrome in a look-up table and retrieved in O(1) time. The proposed flip-syndrome-list (FSL) decoder fully parallelizes all constituent code blocks without sacrificing performance, thus is suitable for ultra-low-latency applications. Meanwhile, two code construction optimizations are presented to further reduce complexity and improve performance, respectively.

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arXiv2018

A 5.16Gbps decoder ASIC for Polar Code in 16nm FinFET

Polar codes has been selected as 5G standard. However, only a couple of ASIC featuring decoders are fabricated,and none of them support list size L > 4 and code length N > 1024. This paper presents an ASIC implementation of three decoders for polar code: successive cancellation (SC) decoder, flexible decoder and ultra-reliable decoder. These decoders are all SC based decoder, supporting list size up to 1,8,32 and code length up to 2^15,2^14,2^11 respectively. This chip is fabricated in a 16nm TSMC FinFET technology, and can be clocked at 1 Ghz. Optimization techniques are proposed and employed to increase throughput. Experiment result shows that the throughput can achieve up to 5.16Gbps. Compared with fabricated AISC decoder and synthesized decoder in literature, the flexible decoder achieves higher area efficiency.

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