Distance spectrum and optimized design of concatenated polar codes

Xu, Minzi; Chen, Peiyao; Bai, Baoming; Tong, Sheng

doi:10.1109/wcsp.2017.8170924

Cited by 10 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Introducing PC bits in the middle of the decoding instead of a single CRC check at the end makes it easier to tune the polar code spectrum; bit-channels corresponding to minimum weight rows are the best candidates to host parity checks [44]. 3GPP decided to adopt a low complexity PC design based on shift registers [45] in conjunction with a classical CRC, as proposed in [46], to improve the code design flexibility. The insertion of an interleaver between the CRC encoder and the polar encoder may have a positive impact on the performance of the code due to the induced change in the number of minimum weight codewords [47].…”

Section: Assistant Bits Designmentioning

confidence: 99%

Design of Polar Codes in 5G New Radio

Bioglio

Condo

Land

2021

IEEE Commun. Surv. Tutorials

220

107

View full text Add to dashboard Cite

Polar codes have attracted the attention of academia and industry alike in the past decade, such that the 5 th generation wireless systems (5G) standardization process of the 3 rd generation partnership project (3GPP) chose polar codes as a channel coding scheme. In this tutorial, we provide a description of the encoding process of polar codes adopted by the 5G standard. We illustrate the struggles of designing a family of polar codes able to satisfy the demands of 5G systems, with particular attention to rate flexibility and low decoding latency. The result of these efforts is an elaborate framework that applies novel coding techniques to provide a solid channel code for NR requirements.

show abstract

Section: Assistant Bits Designmentioning

confidence: 99%

Design of Polar Codes in 5G New Radio

Bioglio

Condo

Land

2021

IEEE Commun. Surv. Tutorials

220

107

View full text Add to dashboard Cite

show abstract

“…where P(t * = t), the probability of correct decoding at the t-th additional attempt, can be obtained by Monte-Carlo simulations, while P FA and P UE , the probabilities related to CRC, can be approximately estimated by the method in [32]. Assume the error probability of the information bit p ∈ [0, 0.5], the AWGN channel with p can be approximately converted into a discrete binary symmetry channel(BSC) with…”

Section: The Performance Analysismentioning

confidence: 99%

“…where A i = |{c|c ∈ C, w(c) = i}| denotes the number of codes c with weight i in the codebook C and k is the information length of CRC-polar codes. The weight distribution A i is obtained by enumerating all short length codewords or SCL with an extremely large list for relatively long length codewords [32]. Using P UE ≤ 2 k − 1 2 −k−r ≤ 2 −r , we get the upper bound of P BSCF according to [32], [33].…”

Section: The Performance Analysismentioning

confidence: 99%

BER Evaluation Based SCFlip Algorithm for Polar Codes Decoding

2020

View full text Add to dashboard Cite

Successive cancellation (SC) decoding of polar codes may bring about error propagation that needs to be mitigated. In this paper, we present a new SC Flipping (SCFlip) decoder, named bit error rate (BER) evaluation based SCFlip (BER-SCFlip), which can accurately target the first error bit and correct it with a high probability. Thus, a high error correction capability and a low decoding complexity can be achieved. First, we propose a new criterion to find out the most suspicious error bit. Those non-frozen bits that have higher decoding BERs derived from log-likelihood-ratios (LLRs) after SC decoding than the corresponding expected ones estimated via Gaussian Approximation (GA), are collected into the flip-bits set. These candidate bits will be flipped one by one according to their SC decoding orderings in extra decoding attempts until the decoded codeword passes cyclic redundancy check (CRC) or a predetermined maximum number of extra attempts is reached. We then propose an extended version of BER-SCFlip, named BER-SCFlip-ω with the capability to correct up to ω error bits in each extra decoding attempt. By combining our criterion for the flip-bits selection with that of Dynamic SCFlip (D-SCFlip), the proposed BER-SCFlip-ω significantly reduces decoding complexity and latency while maintaining the superior error-correction performance close to that of D-SCFlip-ω. The simulation results show that the proposed schemes are competitive among existing SCFlip algorithms and could achieve the error-correction performance approaching that of CRC-aided SCL decoding under list size L = 16 while maintaining low complexity. INDEX TERMS Polar codes, SC decoding, SCFlip decoding, Gaussian approximation.

show abstract

“…An analysis of the CPC based on the WEF and the MacWilliams identity has been recently developed in [27] but with reference to specific codes and then ignoring the (average) impact of different interleavers, that instead we are able to take into account through the study of the ensembles. The latter issue will be discussed in Section IV.…”

Section: A Weight Enumeratorsmentioning

confidence: 99%

Analysis of the Block Error Probability of Concatenated Polar Code Ensembles

Ricciutelli

Jerkovits

Baldi

et al. 2019

IEEE Trans. Commun.

View full text Add to dashboard Cite

In this paper, we provide an analysis of the performance of concatenation of polar codes with outer cyclic redundancy check (CRC) codes, separated by an interleaver, in the short and moderate block length regimes. The analysis addresses maximum likelihood decoding as a proxy to the code performance under successive cancellation list decoding. The analysis is carried out by introducing the concatenated polar code (CPC) ensembles, whose distance properties can be analyzed (for sufficiently short block lengths) by means of the uniform interleaver approach. At moderate block lengths, we resort to the Monte Carlo simulations. Results show that if the inner polar code possesses a low minimum distance and the outer CRC code has a sufficiently large amount of redundancy, then the choice of the outer code generator polynomial and the interleaver may yield to a large variability in the performance of the resulting CPC.

show abstract

Distance spectrum and optimized design of concatenated polar codes

Cited by 10 publications

References 12 publications

Design of Polar Codes in 5G New Radio

Design of Polar Codes in 5G New Radio

BER Evaluation Based SCFlip Algorithm for Polar Codes Decoding

Analysis of the Block Error Probability of Concatenated Polar Code Ensembles

Contact Info

Product

Resources

About