Polar Codes and Polar Lattices for Independent Fading Channels

Liu, Ling; Ling, Cong

doi:10.1109/tcomm.2016.2613109

Cited by 29 publications

(22 citation statements)

References 37 publications

(15 reference statements)

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“…How to design x i to reliably transmit information at the highest rate via a specific channel has been widely and comprehensively studied over the past decades. A branch of this study is to construct capacity-achieving lattice codes for an AWGN channel and its fading variants [28][29][30][31]. At the transmitter's end, lattice coding maps binary codes to a constellation diagram in Euclidean space, called lattice modulation.…”

Section: Channel Modelsmentioning

confidence: 99%

How to Construct Polar Codes for Ring-LWE-Based Public Key Encryption

Wang

Ling

2021

Entropy

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There exists a natural trade-off in public key encryption (PKE) schemes based on ring learning with errors (RLWE), namely: we would like a wider error distribution to increase the security, but it comes at the cost of an increased decryption failure rate (DFR). A straightforward solution to this problem is the error-correcting code, which is commonly used in communication systems and already appears in some RLWE-based proposals. However, applying error-correcting codes to those cryptographic schemes is far from simply installing an add-on. Firstly, the residue error term derived by decryption has correlated coefficients, whereas most prevalent error-correcting codes with remarkable error tolerance assume the channel noise to be independent and memoryless. This explains why only simple error-correcting methods are used in existing RLWE-based PKE schemes. Secondly, the residue error term has correlated coefficients leaving accurate DFR estimation challenging even for uncoded plaintext. It can be found in the literature that a tighter DFR estimation can effectively create a DFR margin. Thirdly, most error-correcting codes are not well designed for safety considerations, e.g., syndrome decoding has a nonconstant time nature. A code good at error correcting might be weak under a variety of attacks. In this work, we propose a polar coding scheme for RLWE-based PKE. A relaxed “independence” assumption is used to derive an uncorrelated residue noise term, and a wireless communication strategy, outage, is used to construct polar codes. Furthermore, some knowledge about the residue noise is exploited to improve the decoding performance. With the parameterization of NewHope Round 2, the proposed scheme creates a considerable DRF margin, which gives a competitive security improvement compared to state-of-the-art benchmarks. Specifically, the security is improved by 28.8%, while a DFR of 2−149 is achieved a for code rate pf 0.25, n=1024,q= 12,289, and binomial parameter k=55. Moreover, polar encoding and decoding have a quasilinear complexity O(Nlog2N) and intrinsically support constant-time implementations.

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Section: Channel Modelsmentioning

confidence: 99%

How to Construct Polar Codes for Ring-LWE-Based Public Key Encryption

Wang

Ling

2021

Entropy

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“…For fading additive exponential noise channels, expansion coding was used in conjunction with polar codes. In 2016, Liu and Ling [19] designed polar codes and polar lattices for independent identically distributed fading channels when the channel state information is not available to the transmitter. For the binary input case, they proposed a design of polar codes through single-stage polarization to achieve the ergodic capacity.…”

Section: Introductionmentioning

confidence: 99%

Performance of Polar Codes over Generalized Correlated Fading Channels

Barros

Oliveira²,

Alcoforado³

et al. 2022

JCIS

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Polar coding, as introduced by Arikan in 2009, is an error correcting code scheme that uses the polarization technique to obtain almost noise-free channels that are suitable for transmission. Polar codes are being widely studied due to their applications on the 5th Generation (5G) of mobile communication systems. In 5G communications, the wireless channel is subject to fading that can significantly degrade the quality of the transmitted signals. In this context, the generalized fading models are useful due to their capacity to model a variety channel conditions ranging from moderate to severe fading by adjusting some parameters. In this work, the authors investigate the performance of polar codes considering the transmission over generalized fading channels. Additionally, the effect of channel correlation is analyzed and a random interleaver is proposed to mitigate the negative impact of the correlation on the system performance. For the system with generalized fading modeled by η-µ distribution and Cyclic Redundancy Check (CRC) Aided Successive Cancellation List (CA-SCL) decoding, the scenario with correlated fading channel and interleaving shows a performance improvement compared to the system without interleaving. In this case, a gain of approximately 3.5 dB is obtained considering a Bit Error Rate (BER) of 10 −2 . Considering the α-µ (α = 2 and µ = 1) and the κ-µ (κ = µ = 2) fading channels, the uncorrelated systems outperform the correlated ones. Among them, the interleaver improves the performance of the systems. For BER of 10 −2 , as an example, the use of fading correlated channel and interleaver shows a performance improvement of 12 dB and 0.5 dB for the α-µ and κ-µ fading channels, respectively.

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“…The different bit levels of SSK are shown to have quite different bit-level capacities, which further motivates our approach. For the sake of simplicity of the system design, we have designed the polar code for an average-case scenario of the Rayleigh fading channel using the method given in [10]. Our simulation results show that at a bit error rate (BER) of 10 −4 , the designed MLC polar coded 16 × 1 SSK system exhibits a gain of 2.9 dB over the corresponding system using BICM.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Polar Coded Space-Shift Keying

Hasan¹,

Perović²,

Flanagan³

2021

Preprint

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Multilevel coding (MLC) is a coded modulation technique which can achieve excellent performance over a range of communication channels. Polar codes have been shown to be quite compatible with communication systems using MLC, as the rate allocation of the component polar codes follows the natural polarization inherent in polar codes. MLC based techniques have not yet been studied in systems that use spatial modulation (SM). SM makes the polar code design difficult as the spatial bits actually select a channel index for transmission. To solve this problem, we propose a Monte Carlo based evaluation of the ergodic capacities for the individual bit levels under the capacity rule for a space-shift keying (SSK) system, where we also make use of a single antenna activation to approximate the transmission channel for the design of the multilevel polar code. Our simulation results show that the multilevel polar coded 16×1 SSK system outperforms the corresponding system that uses bitinterleaved polar coded modulation by 2.9 dB at a bit-error rate (BER) of 10 −4 .

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Polar Codes and Polar Lattices for Independent Fading Channels

Cited by 29 publications

References 37 publications

How to Construct Polar Codes for Ring-LWE-Based Public Key Encryption

How to Construct Polar Codes for Ring-LWE-Based Public Key Encryption

Performance of Polar Codes over Generalized Correlated Fading Channels

Multilevel Polar Coded Space-Shift Keying

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