Multi-kernel construction of polar codes

Gabry, Frédéric; Bioglio, Valerio; Land, Ingmar; Belfiore, Jean-Claude

doi:10.1109/iccw.2017.7962750

Cited by 73 publications

(79 citation statements)

References 14 publications

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“…Utilization of alternate polarizing matrices, known as kernels, in the formulation for G was proposed in [9] and outlined the possibility of obtaining polar codes that are not constrained to lengths that are powers of 2. The ternary kernel T 3 = 1 1 1 1 0 1 0 1 1 was proposed as the 3 × 3 polarizing matrix.…”

Section: A Multi-kernel Polar Codesmentioning

confidence: 99%

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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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Section: A Multi-kernel Polar Codesmentioning

confidence: 99%

“…PC(18,9) with G = T2 ⊗ T3 ⊗ T3 PC(18, 11) with G = T3 ⊗ T3 ⊗ T2 SC decoding trees (light grey) which are pruned to their Fast-SSC counterparts (black). White and grey leaf nodes represent frozen and information bits, respectively.…”

mentioning

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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“…MK polar codes were introduced in [6] as an alternative polarizing construction to attain polar codes of lengths other than powers of 2. The ternary kernel T 3 = 1 1 1 1 0 1 0 1 1…”

Section: Multi-kernel Polar Codesmentioning

confidence: 99%

Asymmetric Construction of Low-Latency and Length-Flexible Polar Codes

Cavatassi

Tonnellier

Gross

2019

ICC 2019 - 2019 IEEE International Conference on Communications (ICC)

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Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5 th generation (5G) wireless standard. Most polar code research examines the original Arıkan polar coding scheme, which is limited in block length to powers of two. This constraint presents a considerable obstacle since practical applications call for all code lengths to be readily available. Puncturing and shortening techniques allow for flexible polar codes, while multi-kernel polar codes produce native code lengths that are powers of two and/or three. In this work, we propose a new low complexity coding scheme called asymmetric polar coding that allows for any arbitrary block length. We present details on the generator matrix, frozen set design, and decoding schedule. Our scheme offers flexible polar code lengths with decoding complexity lower than equivalent state-of-the-art length-compatible approaches under successive cancellation decoding. Further, asymmetric decoding complexity is directly dependent on the codeword length rather than the nearest valid polar code length. We compare our scheme with other length matching techniques, and simulations are presented. Results show that asymmetric polar codes present similar error correction performance to the competing schemes, while dividing the number of SC decoding operations by up to a factor of 2 using the same codeword length.

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“…and the recursive structure of the matrix is highlighted. The frozen set F indicates the N − K bits to be frozen in the code construction, and can generally be designed according to bit reliabilities [4] or minimum distance [14]. Finally, the encoder is defined by i / ∈ F , stores the information bits.…”

Section: Multi-kernel Polar Codesmentioning

confidence: 99%

“…Puncturing and shortening techniques can be used to adjust the code length, at the cost of a reduced bit polarization [3]. To overcome this limitation, multi-kernel polar codes have been introduced in [4]. By mixing binary kernels of different sizes in the construction of the code, these codes prove that many block lengths can be achieved while keeping the polarization effect.…”

Section: Introductionmentioning

confidence: 99%

Memory Management in Successive-Cancellation based Decoders for Multi-Kernel Polar Codes

Bioglio

Condo

Land

2018

2018 52nd Asilomar Conference on Signals, Systems, and Computers

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Multi-kernel polar codes have recently been proposed to construct polar codes of lengths different from powers of two. Decoder implementations for multi-kernel polar codes need to account for this feature, that becomes critical in memory management. We propose an efficient, generalized memory management framework for implementation of successivecancellation decoding of multi-kernel polar codes. It can be used on many types of hardware architectures and different flavors of SC decoding algorithms. We illustrate the proposed solution for small kernel sizes, and give complexity estimates for various kernel combinations and code lengths.

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Multi-kernel construction of polar codes

Cited by 73 publications

References 14 publications

Fast Decoding of Multi-Kernel Polar Codes

Fast Decoding of Multi-Kernel Polar Codes

Asymmetric Construction of Low-Latency and Length-Flexible Polar Codes

Memory Management in Successive-Cancellation based Decoders for Multi-Kernel Polar Codes

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