On Probabilistic Weight Distribution of Polar Codes

Valipour, Mehrdad; Yousefi, Shahram

doi:10.1109/lcomm.2013.091113.131213

Cited by 30 publications

(21 citation statements)

References 13 publications

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“…i-polar code is obtained by the recursive equation (5). The average WEF of the concatenated code is obtained as follows.…”

Section: A Analytical and Simulation Results Of I-polar Codes And Pomentioning

confidence: 99%

“…Table I gives the coefficients of WEFs of all test cases, of which the Hamming weights, denoted as d, are listed in the first column and the remaining columns are the coefficients A d of all test cases. The WEF averaged over the ensemble of i-polar codes is denoted as WEF(A), which is computed based on the recursive equation (5). Since the code size is small, the WEF of a realization of i-polar codes can be enumerated exhaustively.…”

Section: Wefs Of (32 16) I-polar Code and Polar Codementioning

confidence: 99%

“…The parameters d min and A d min for the i-polar and polar codes with N = 512 and K varying from 32 to 480 are shown in Figure 5. The parameters d min and A d min for i-polar codes are obtained through the recursive equation (5). Since there are no analytical WEFs for polar codes, we use the SCL decoder with L = 5 × 10 5 to search for the minimum weight codewords as that proposed in [3].…”

Section: Wefs Of (32 16) I-polar Code and Polar Codementioning

confidence: 99%

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Interleaved Polar (I-Polar) Codes

Chiu

2020

IEEE Trans. Inform. Theory

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By inserting interleavers between intermediate stages of the polar encoder, a new class of polar codes, termed interleaved polar (i-polar) codes, is proposed. By the uniform interleaver assumption, we derive the weight enumerating function (WEF) and input-output weight enumerating function (IOWEF) averaged over the ensemble of i-polar codes. The average WEF can be used to calculate the upper bound on the average block error rate (BLER) of a code selected at random from the ensemble of i-polar codes. Also, we propose a concatenated coding scheme that employs P high rate codes as the outer code and Q i-polar codes as the inner code with an interleaver in between. The average WEF of the concatenated code is derived based on the uniform interleaver assumption. Simulation results show that BLER upper bounds can well predict BLER performance levels of the concatenated codes. The results show that the performance of the proposed concatenated code with P = Q = 2 is better than that of the CRC-aided i-polar code with P = Q = 1 of the same length and code rate at high signalto-noise ratios (SNRs). Moreover, the proposed concatenated code allows multiple decoders to operate in parallel, which can reduce the decoding latency and hence is suitable for ultra-reliable low-latency communications (URLLC).

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“…i-polar code is obtained by the recursive equation (5). The average WEF of the concatenated code is obtained as follows.…”

Section: A Analytical and Simulation Results Of I-polar Codes And Pomentioning

confidence: 99%

Section: Wefs Of (32 16) I-polar Code and Polar Codementioning

confidence: 99%

Section: Wefs Of (32 16) I-polar Code and Polar Codementioning

confidence: 99%

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Interleaved Polar (I-Polar) Codes

Chiu

2020

IEEE Trans. Inform. Theory

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“…where A out i is the weight enumerator of the outer code and A IO,in i,ω is the input-output weight enumerator of the inner code (we remind that the average multiplicities resulting from (8) are, in general, real numbers).…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…In this work we have assumed ξ = 0.99, hence at least one code belongs to the good codes ensemble. Therefore, when the expurgation method is adoptable (i.e., the first term of the AWEF has a codewords multiplicity less than ξ), through (7) and (8) the average performance of the good codes subset is derived.…”

Section: Notation and Definitionsmentioning

confidence: 99%

On the error probability of short concatenated polar and cyclic codes with interleaving

Ricciutelli

Baldi

Chiaraluce

et al. 2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Abstract-In this paper, the analysis of the performance of the concatenation of a short polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is employed together with an inner systematic polar code. A concatenated code ensemble is introduced placing an interleaver at the input of the polar encoder. The introduced ensemble allows deriving bounds on the achievable error rates under maximum likelihood decoding, by applying the union bound to the (expurgated) average weight enumerators. The analysis suggests the need of careful optimization of the outer code, to attain low error floors.

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Fast decoding of polar codes using tree structure

Andi

Gazi

2019

IET Communications

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On Probabilistic Weight Distribution of Polar Codes

Cited by 30 publications

References 13 publications

Interleaved Polar (I-Polar) Codes

Interleaved Polar (I-Polar) Codes

On the error probability of short concatenated polar and cyclic codes with interleaving

Fast decoding of polar codes using tree structure

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