Research on Polar Code Construction Algorithms Under Gaussian Channel

Li, Jianping; Hu, Man; Cheng, Zhiyuan

doi:10.1109/icufn.2018.8437011

Cited by 9 publications

(14 citation statements)

References 6 publications

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“…In Fig. 3 we can see the compound function (15), which we will call the modified Gaussian and its behavior when we vary the mean, since tanh does not depend on the mean. Each curve is a Gaussian function with an mean ranging from 0 to 15.…”

Section: Proposed Construction Based On Piecewise Gaussian Approximationmentioning

confidence: 99%

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Study of Polar Codes Based on Piecewise Gaussian Approximation

Oliveira¹,

Lamare

2021

Preprint

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In this paper, we investigate the construction of polar codes by Gaussian approximation (GA) and develop an approach based on piecewise Gaussian approximation (PGA). In particular, with the piecewise approach we obtain a function that replaces the original GA function with a more accurate approximation, which results in significant gain in performance. The proposed PGA construction of polar codes is presented in its integral form as well as an alternative approximation that does not rely on the integral form. Simulations results show that the proposed PGA construction outperforms the standard GA for several examples of polar codes and rates.

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Section: Proposed Construction Based On Piecewise Gaussian Approximationmentioning

confidence: 99%

“…The authors in [11], [12] and [13] proposed improved Gaussian approximations for long blocks with better performance than AGA. Examples of algorithms for implementing the GA can be found in [14] and [15].…”

Section: Introductionmentioning

confidence: 99%

Study of Polar Codes Based on Piecewise Gaussian Approximation

Oliveira¹,

Lamare

2021

Preprint

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“…Both in [9] and in [10] they show a comparative study of the PC construction, their algorithm complexity and their performance. The scenario used is the AWGN channel and SC and SCL decoders for various rates and codewords.…”

Section: Introdutionmentioning

confidence: 99%

Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

Oliveira

Lamare²

2021

IEEE Access

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In this paper we propose a technique for polar codes (PC) construction for any code length. By default, PC construction is limited to code length proportional to the power of two. To construction the code length arbitrary, puncturing, shortening and extension techniques must be applied. However, performance is degraded with the use of these techniques. Other ways to design polar codes with arbitrary code length but which have encoding and decoding with higher complexity such as multi-kernel, concatenated codes and specific constructions for belief propagation (BP) or successive cancellation list (SCL) decoding. The polarization theory [1] is generalized for non-uniform channels (NUC) and with this approach we can construction rate-compatible PC and variable code length. We developed an implementation algorithm based on the of PC construction by Gaussian approximation (NUPGA). In a scenario where the transmission is over an additive white Gaussian noise (AWGN) channel and under successive cancellation (SC) decoding, the PC construction of arbitrary code length can be implemented with NUPGA. With NUPGA we repolarize the projected synthetic channels by choosing more efficiently the positions of the information bits. In addition, we present a generalization of the Gaussian approximation (GA) for the polarization and repolarization processes and an extension technique for PC. The PC construction based on NUPGA present better performance than the existing techniques as shown in the simulations of this work.

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“…This can be used to simplify code construction of polar codes. In [9] and [10] a comparative study of the performance of polar codes constructed by various techniques using the AWGN channel and SC decoder has been carried out. Construction of polar codes based on the AWGN channel and GA have been reported in [11] and [12].…”

Section: Introdutionmentioning

confidence: 99%

Study of Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

Oliveira,

de Lamare

2021

Preprint

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We propose a novel scheme for rate-compatible arbitrarylength polar code construction for the additive white Gaussian noise (AWGN) channel. The proposed scheme is based on the concept of nonuniform channel polarization. The original polar codes can only be designed with code lengths that are powers of two. Puncturing, shortening and extension are three strategies to obtain arbitrary code lengths and code rates for polar codes. There are other ways to design codes with arbitrary length but which have encoding and decoding with higher complexity such as multi-kernel, concatenated codes and specific constructions for Belief propagation (BP) or Successive Cancellation (SC) decoding. In general, the quality of the projected bit channels by these arbitrary-length techniques differs from that of the original bit channels, which can greatly affect the performance of the constructed polar codes. The proposed Non-Uniform Polarization based on Gaussian Approximation (NUPGA) is an efficient construction technique for rate-compatible arbitrary-length polar codes, which chooses the best channels (i.e., selects the positions of the information bits) by re-polarization of the codeword with desired length. A generalization of the Gaussian Approximation is devised for both polarization and re-polarization processes. We also present shortening and extension techniques for design polar codes. Simulations verify the effectiveness of the proposed NUPGA designs against existing rate-compatible techniques.

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Research on Polar Code Construction Algorithms Under Gaussian Channel

Cited by 9 publications

References 6 publications

Study of Polar Codes Based on Piecewise Gaussian Approximation

Study of Polar Codes Based on Piecewise Gaussian Approximation

Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

Study of Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

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