Polar Subcodes

Trifonov, Peter; Miloslavskaya, Vera

doi:10.1109/jsac.2015.2504269

Cited by 116 publications

(99 citation statements)

References 45 publications

(98 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Figure 5, the code with N r = 512 is compared to those with N = 1024 and N = 2048, for both SC and SCL-based decoding. Four vertical lines are shown, indicating the E b /N 0 from which the proposed decoding is faster than standard SC and SCL decoding of codes of length N = 1024 and N = 2048, according to (10) and (11). It can be seen that at these E b /N 0 points, the proposed decoding approach has substantially lower BER than its competitor.…”

Section: Performance Resultsmentioning

confidence: 98%

Practical Product Code Construction of Polar Codes

Condo

Bioglio

Hafermann

et al. 2020

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets of the component polar codes. Moreover, we show how polar codes can be described as irregular product codes. We propose a two-step decoder for long polar codes taking advantage of this dual nature to heavily reduce decoding latency. Finally, we show that the proposed decoding technique outperforms both standard polar codes and state-of-the-art codes for optical communications under latency constraints.

show abstract

Section: Performance Resultsmentioning

confidence: 98%

Practical Product Code Construction of Polar Codes

Condo

Bioglio

Hafermann

et al. 2020

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…There also exist several Monte-Carlo-based designs for specific decoding schemes. Additionally, various schemes focus on improving the finite-length performance of polar codes either by interpolating them using other codes (e.g., Reed-Muller (RM)-codes), to enjoy good finite-performance provided by these codes [23], [24] or via concatenation schemes with other codes, e.g., [25]- [27].…”

Section: Code Construction Mismatch Paradigmmentioning

confidence: 99%

Optimizing Polar Codes Compatible with Off-the-Shelf LDPC Decoders

Ebada

Elkelesh

Brink

2019

2019 IEEE Information Theory Workshop (ITW)

View full text Add to dashboard Cite

Previous work showed that polar codes can be decoded using off-the-shelf LDPC decoders by imposing special constraints on the LDPC code structure, which, however, resulted in some performance degradation. In this paper we show that this loss can be mitigated; in particular, we demonstrate how the gap between LDPC-style decoding and Arıkan's Belief Propagation (BP) decoding of polar codes can be closed by taking into account the underlying graph structure of the LDPC decoder while jointly designing the polar code and the parity-check matrix of the corresponding LDPC-like code. The resulting polar codes under conventional LDPC-style decoding are shown to have similar error-rate performance when compared to some well-known and standardized LDPC codes. Moreover, we obtain performance gains in the high SNR region.

show abstract

“…It was suggested in [3] to set frozen symbols u i , i ∈ F not to zero, but to linear combinations of some other symbols, i.e.…”

Section: A Polar Codes and Polar Subcodesmentioning

confidence: 99%

“…August 23, 2018 DRAFT F. (16,10,4), (16,11,4) and (16,12,2) codes These codes, obtained by Plotkin concatenation of (8,4,4) or (8,3,4) codes and (8, 7, 2) or (8, 8, 1) codes, commonly arise in the GPD of polar codes. Decoding of these codes can be implemented using the approach introduced in [23].…”

Section: E Double Parity Check Codesmentioning

confidence: 99%

See 1 more Smart Citation

Block sequential decoding of polar codes

Trofimiuk

Trifonov

2015

2015 International Symposium on Wireless Communication Systems (ISWCS)

Self Cite

View full text Add to dashboard Cite

A reduced complexity sequential decoding algorithm for polar subcodes is described. The proposed approach relies on a decomposition of the polar (sub)code into a number of outer codes, and on-demand construction of codewords of these codes in the descending order of their probability. The proposed algorithm can be also used for decoding of polar codes with CRC and short extended BCH codes. It has lower average decoding complexity compared to the existing decoding algorithms for the corresponding codes.where V is a (n − k) × n binary matrix, such that its rows end in distinct columns, and j i is the index of row with the last non-zero element in column i. Such symbols with non-trivial right hand side expressions are called dynamic frozen, and the corresponding codes are referred to as polar subcodes. Decoding of such codes can be implemented by a straightforward generalization of the successive cancellation algorithm and its derivatives.Properly constructed polar subcodes may have higher minimum distance than classical polar codes. This results in substantially better performance [3], [10] under the list SC algorithm and its derivatives. Polar codes with CRC [2] can be considered as a special case of polar subcodes.

show abstract

Polar Subcodes

Cited by 116 publications

References 45 publications

Practical Product Code Construction of Polar Codes

Practical Product Code Construction of Polar Codes

Optimizing Polar Codes Compatible with Off-the-Shelf LDPC Decoders

Block sequential decoding of polar codes

Contact Info

Product

Resources

About