Construction and Block Error Rate Analysis of Polar Codes Over AWGN Channel Based on Gaussian Approximation

Wu, Daolong; Li, Ying; Sun, Yue

doi:10.1109/lcomm.2014.2325811

Cited by 184 publications

(114 citation statements)

References 9 publications

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“…However, neither of these papers clearly explains why this method works. We found the explanation in [22] by D. Wu, Y. Li, and Y. Sun.…”

Section: Gaussian Approximation Methods For Awgn Channelsmentioning

confidence: 53%

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Polar Codes

Wasserman¹

2014

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“…However, neither of these papers clearly explains why this method works. We found the explanation in [22] by D. Wu, Y. Li, and Y. Sun.…”

Section: Gaussian Approximation Methods For Awgn Channelsmentioning

confidence: 53%

“…However, [22] claims that this procedure computes P (C i ), defined as the conditional probability of a real (i.e., not genie-aided) SC decoder incorrectly decoding the ith bit, subject to the condition that all previous bits are decoded correctly. The BLER is then computed as 1 − i∈A (1 − P (C i )).…”

Section: Error In Wu LI and Sunmentioning

confidence: 99%

Polar Codes

Wasserman¹

2014

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“…, q. Let us compute the numerator in (22). We can view T q (r) ∩ H q as a new simplex obtained by moving the origin to the point A = (− r 2 , .…”

Section: Channel Degradation and The Code Construction Schemementioning

confidence: 99%

“…We obtain Vol(Sq) = Now let us turn to the denominator in (22). Note that B 1 (y i ) ⊇ B 2 (y i ), where B 2 (y i ) is an 2 ball of radius r 2 √ q centered at P W (·|y i ).…”

Section: Channel Degradation and The Code Construction Schemementioning

confidence: 99%

Construction of Polar Codes for Arbitrary Discrete Memoryless Channels

Gulcu

Barg

2018

IEEE Trans. Inform. Theory

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It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for the general case, and analyze an algorithm that is based on successive reduction of the output alphabet size of the subchannels in each recursion step. For this procedure we estimate the approximation error as O(µ −1/(q−1) ), where µ is the "quantization parameter," i.e., the maximum size of the subchannel output alphabet allowed by the algorithm. The complexity of the code construction scales as O(N µ 2 log µ), where N is the length of the code. We also show that if the polarizing operation relies on modulo-q addition, it is possible to merge subsets of output symbols without any loss in subchannel capacity. Performing this procedure before each approximation step results in a further speed-up of the code construction, and the resulting codes have smaller gap to capacity. We also show that a similar acceleration can be attained for polar codes over finite field alphabets.Experimentation shows that the suggested construction algorithms can be used to construct long polar codes for alphabets of size q = 16 and more with acceptable loss of the code rate for a variety of polarizing transforms.

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“…Except for the binary erasure channel (BEC) under successive cancellation (SC) decoding, there is no optimal frozen bits selection method for B-DMCs like the AWGN channel so far. Therefore, it is valuable that some calculation-based selection algorithms were proposed, such as the density evolution (DE) and Gaussian approximation (GA) algorithms [2,3,4,5]. These algorithms achieved similar performance compared with the heuristic manner Arikan introduced in [6].…”

Section: Introductionmentioning

confidence: 99%

Frozen bits selection for polar codes based on simulation and BP decoding

Liu

Sha

2017

IEICE Electron. Express

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In the construction of polar code, the selection of frozen bits affects the error-correcting performance significantly. Several calculationbased algorithms have been proposed for general binary-input discrete memoryless channels (B-DMCs) like the additive white Gaussian noise (AWGN) channel. In this paper, a method for frozen bits selection based on Monte Carlo simulation and belief propagation (BP) decoding is proposed. The information bits are selected out one by one incrementally. The numerical results show that the proposed algorithm can effectively improve the bit error rate (BER) and frame error rate (FER) performance compared with the conventional selection method, especially in high signal noise ratio (SNR) region. Moreover, the algorithm can be used to construct polar codes with any rate through a complete iteration.

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Construction and Block Error Rate Analysis of Polar Codes Over AWGN Channel Based on Gaussian Approximation

Cited by 184 publications

References 9 publications

Polar Codes

Polar Codes

Construction of Polar Codes for Arbitrary Discrete Memoryless Channels

Frozen bits selection for polar codes based on simulation and BP decoding

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