Linear and Nonlinear Binary Kernels of Polar Codes of Small Dimensions With Maximum Exponents

Lin, Hsien-Ping; Lin, Shu; Abdel-Ghaffar, Khaled

doi:10.1109/tit.2015.2469298

Cited by 50 publications

(40 citation statements)

References 20 publications

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“…In Lemma 1, we suppose the kernel G m is a lower triangular matrix since all of optimal kernels given in [6] are lower triangular matrices. In fact, we don't need lower triangular assumption in Lemma 1.…”

Section: B High-level Description Of the Algorithmmentioning

confidence: 99%

“…Then the complexity of W -expressions based SC decoder is O(C W (m) ⋅ mN log N m ) for the G m based polar code. Table II gives the results of C W (m) by using Algorithm 2 for optimal kernels [6] up to m = 16. It means that the complexity of W -expressions based SC decoder is O(m 2 N log N ) when m ≤ 16.…”

Section: Complexity Analysis Of W -Expressionsmentioning

confidence: 99%

“…So, similar to l-expressions, we propose a W -expressions method to further reduce the complexity of SC decoder for larger dimension kernels by considering bit-channel transition probabilities W (⋅) G (⋅ 0) and W (⋅) G (⋅ 1) separately. Our main achievement is: Using W -expressions method, we show that the complexity of G m SC decoder is O(m 2 N log N ) for optimal kernels given in [6] when m ≤ 16.…”

Section: Introductionmentioning

confidence: 99%

“…In [5], code decompositions were used to design good linear and nonlinear binary kernels. In [6], constructions were presented for kernels with maximum exponents up to dimension 16. Fig.…”

Section: Introductionmentioning

confidence: 99%

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Simplified Successive Cancellation Decoding of Polar Codes With Medium-Dimensional Binary Kernels

Huang

Zhang

et al. 2018

IEEE Access

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A method for efficiently successive cancellation (SC) decoding of polar codes with high-dimensional linear binary kernels (HDLBK) is presented and analyzed. We devise a lexpressions method which can obtain simplified recursive formulas of SC decoder in likelihood ratio form for arbitrary linear binary kernels to reduce the complexity of corresponding SC decoder. By considering the bit-channel transition probabilities W (⋅) G (⋅ 0) and W (⋅) G (⋅ 1) separately, a W -expressions method is proposed to further reduce the complexity of HDLBK based SC decoder. For a m × m binary kernel, the complexity of straightforward SC decoder is O(2 m N log N ). With W -expressions, we reduce the complexity of straightforward SC decoder to O(m 2 N log N ) when m ≤ 16. Simulation results show that 16×16 kernel polar codes offer significant advantages in terms of error performances compared with 2 × 2 kernel polar codes under SC and list SC decoders.

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Section: B High-level Description Of the Algorithmmentioning

confidence: 99%

Section: Complexity Analysis Of W -Expressionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In [5], code decompositions were used to design good linear and nonlinear binary kernels. In [6], constructions were presented for kernels with maximum exponents up to dimension 16. Fig.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simplified Successive Cancellation Decoding of Polar Codes With Medium-Dimensional Binary Kernels

Huang

Zhang

et al. 2018

IEEE Access

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“…Specifically, a ternary 3 × 3 matrix was proposed, and so MK polar codes can have lengths that are powers of two, powers of three, or a product of both. Although additional polarizing matrices of larger sizes have been proposed [8], among them the 3 × 3 matrix offers a desirable combination of a sufficiently high polarization exponent and only a small increase in decoding complexity.…”

Section: Introductionmentioning

confidence: 99%

Fast Decoding of Multi-Kernel Polar Codes

Cavatassi

Tonnellier

Gross

2019

2019 IEEE Wireless Communications and Networking Conference (WCNC)

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Polar codes are a class of linear error correction codes which provably attain channel capacity with infinite codeword lengths. Finite length polar codes have been adopted into the 5th Generation 3GPP standard for New Radio, though their native length is limited to powers of 2. Utilizing multiple polarizing matrices increases the length flexibility of polar codes at the expense of a more complicated decoding process. Successive cancellation (SC) is the standard polar decoder and has time complexity O(N log N ) due to its sequential nature. However, some patterns in the frozen set mirror simple linear codes with low latency decoders, which allows for a significant reduction in SC latency by pruning the decoding schedule. Such fast decoding techniques have only previously been used for traditional Arıkan polar codes, causing multi-kernel polar codes to be an impractical length-compatibility technique with no fast decoders available. We propose fast simplified successive cancellation decoding node patterns, which are compatible with polar codes constructed with both the Arıkan and ternary kernels, and generalization techniques. We outline efficient implementations, made possible by imposing constraints on ternary node parameters. We show that fast decoding of multi-kernel polar codes has at least 72% reduced latency compared with an SC decoder in all cases considered where codeword lengths are (96, 432, 768, 2304).

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A Latency and Throughput Efficient Successive Cancellation Decoding of Polar Codes

Manasa

Narayanan

2019

Communications in Computer and Information Science

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Linear and Nonlinear Binary Kernels of Polar Codes of Small Dimensions With Maximum Exponents

Cited by 50 publications

References 20 publications

Simplified Successive Cancellation Decoding of Polar Codes With Medium-Dimensional Binary Kernels

Simplified Successive Cancellation Decoding of Polar Codes With Medium-Dimensional Binary Kernels

Fast Decoding of Multi-Kernel Polar Codes

A Latency and Throughput Efficient Successive Cancellation Decoding of Polar Codes

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