Polar Code Constructions Based on LLR Evolution

Qin, Minghai; Guo, Jing; Bhatia, Aman; Fàbregas, Albert Guillén i; Siegel, Paul H.

doi:10.1109/lcomm.2017.2656126

Cited by 42 publications

(41 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [23], an LLR-based polar code construction is proposed, in which the LLRs of the non-frozen bits are tracked during BP decoding to identify weak information bit-channels, and then the information set A is modified by swapping these weak information bit-channels with strong frozen bit-channels. The resulting code shows an enhanced error-rate performance under both BP and SCL decoding due to the resultant reduction in the number of low weight codewords.…”

Section: Polar Code Constructionmentioning

confidence: 99%

“…The weight enumerator A d is the number of codewords with weight d. There is no closed-form expression for the weight enumerators of polar codes [23]. However, an algorithm proposed in [52] can be used to find the number of minimum-weight codewords (i.e., A d min ).…”

Section: F Weight Enumerators a Dmentioning

confidence: 99%

“…Except for the Binary Erasure Channel (BEC), existing polar code constructions rely either on analytic approximations/bounds such as the Bhattacharyya parameter [2], density evolution [15] and Gaussian approximation [16], [17] or heuristics [18]- [20], including Monte-Carlo-based simulations for specific decoding algorithms [21]- [23]. Additionally, several concatenation schemes of polar codes and other coding techniques have been proposed [24]- [28] to improve the finite length performance under different decoders.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Decoder-Tailored Polar Code Design Using the Genetic Algorithm

Elkelesh

Ebada

Cammerer

et al. 2019

IEEE Trans. Commun.

View full text Add to dashboard Cite

We propose a new framework for constructing polar codes (i.e., selecting the frozen bit positions) for arbitrary channels, and tailored to a given decoding algorithm, rather than based on the (not necessarily optimal) assumption of successive cancellation (SC) decoding. The proposed framework is based on the Genetic Algorithm (GenAlg), where populations (i.e., collections) of information sets evolve successively via evolutionary transformations based on their individual error-rate performance. These populations converge towards an information set that fits both the decoding behavior and the defined channel. Using our proposed algorithm over the additive white Gaussian noise (AWGN) channel, we construct a polar code of length 2048 with code rate 0.5, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding, and leading to a coding gain of 1 dB at BER of 10 −6 . Further, a belief propagation (BP)-tailored construction approaches the SCL error-rate performance without any modifications in the decoding algorithm itself. The performance gains can be attributed to the significant reduction in the total number of low-weight codewords. To demonstrate the flexibility, coding gains for the Rayleigh channel are shown under SCL and BP decoding. Besides improvements in error-rate performance, we show that, when required, the GenAlg can be also set up to reduce the decoding complexity, e.g., the SCL list size or the number of BP iterations can be reduced, while maintaining the same error-rate performance.

show abstract

Section: Polar Code Constructionmentioning

confidence: 99%

Section: F Weight Enumerators a Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Decoder-Tailored Polar Code Design Using the Genetic Algorithm

Elkelesh

Ebada

Cammerer

et al. 2019

IEEE Trans. Commun.

View full text Add to dashboard Cite

show abstract

“…The state-of-the-art polar code constructions (e.g., [12], [25]- [29]) assume that a hard-output SC decoder is used. Thus, these algorithms are not optimal for iterative decoding and list decoding [30]- [32]. The BP decoder has a different decoding strategy when compared to the SC decoder.…”

Section: Code Construction Mismatch Paradigmmentioning

confidence: 99%

Deep Learning-Based Polar Code Design

Ebada

Cammerer

Elkelesh

et al. 2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

View full text Add to dashboard Cite

In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a neural network (NN). For this, we demonstrate how this binary vector can be relaxed to a soft-valued vector, facilitating the learning process through gradient descent and enabling an efficient code construction. We further show how different polar code design constraints (e.g., code rate) can be taken into account by means of careful binary-to-soft and soft-to-binary conversions, along with rate-adjustment after each learning iteration. Besides its conceptual simplicity, this approach benefits from having the "decoder-in-the-loop", i.e., the nature of the decoder is inherently taken into consideration while learning (designing) the polar code. We show results for belief propagation (BP) decoding over both AWGN and Rayleigh fading channels with considerable performance gains over state-of-the-art construction schemes.

show abstract

“…In [9], it was shown that BP decoding of polar codes can be enhanced by appending a short-length LDPC code to the semi-polarized bit channels of the polar code. In [10], the selection of information and frozen bit channels was altered based on log-likelihood ratio (LLR)-evolution leading to a considerable performance gain. Though these approaches push the performance of BP-based decoding of polar codes a bit forward, the gap between their performance compared to that of SCL decoding is, however, still quite large.…”

Section: Introductionmentioning

confidence: 99%

Belief Propagation List Decoding of Polar Codes

et al. 2018

View full text Add to dashboard Cite

We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size L. The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are lower decoding latency compared to the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.

show abstract

Polar Code Constructions Based on LLR Evolution

Cited by 42 publications

References 13 publications

Decoder-Tailored Polar Code Design Using the Genetic Algorithm

Decoder-Tailored Polar Code Design Using the Genetic Algorithm

Deep Learning-Based Polar Code Design

Belief Propagation List Decoding of Polar Codes

Contact Info

Product

Resources

About