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Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels [article]

Hsin-Po Wang, Iwan Duursma
2018 arXiv   pre-print
A pruned variant of polar coding is reinvented for all binary erasure channels.  ...  This result also follows if one applies systematic polar coding [Arıkan 10.1109/LCOMM.2011.061611.110862] with simplified successive cancelation decoding [Alamdar-Yazdi-Kschischang 10.1109/LCOMM.2011.101811.111480  ...  For instance, Lemma 3 implies (N, R, P, bC) (1) = Ä N, Capacity − N −1/5 , 2 −N 1/24 , O(log N ) ä . (2) We provide a pruned variant of polar codes parametrized by over arbitrary binary erasure channels  ... 
arXiv:1812.08106v1 fatcat:mfax67rzczdwff6c7xx5cgpjri

Log-logarithmic Time Pruned Polar Coding

Hsin-Po Wang, Iwan M. Duursma
2020 IEEE Transactions on Information Theory  
A pruned variant of polar coding is proposed for binary erasure channel (BEC). Fix any BEC.  ...  Over general channels, this family of codes has the lowest per-bit time complexity among all capacity-achieving codes known to date.  ...  Among them the most significant one is that Reed-Muller codes achieve capacity under the maximum a posteriori (MAP) decoding over binary erasure channels (BEC) by Kudekar et al. published in 2017 [11  ... 
doi:10.1109/tit.2020.3041523 fatcat:ii3k5ibdabd7vjszqngut5lvm4

Sublinear Latency for Simplified Successive Cancellation Decoding of Polar Codes [article]

Marco Mondelli, Seyyed Ali Hashemi, John Cioffi, Andrea Goldsmith
2020 arXiv   pre-print
This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang.  ...  More specifically, the latency of SSC decoding is O(N^1-1/μ), where N is the block length and μ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity.  ...  Recently, a variant of polar codes with log-logarithmic time complexity per information bit has been introduced in [26] .  ... 
arXiv:1909.04892v2 fatcat:dx2fizupsjggvil7frk6vkglom

Enabling complexity-performance trade-offs for successive cancellation decoding of polar codes

Alexios Balatsoukas-Stimming, Georgios Karakonstantis, Andreas Burg
2014 2014 IEEE International Symposium on Information Theory  
Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest.  ...  In this paper, we propose a systematic method for enabling complexity-performance trade-offs by constructing polar codes based on an optimization problem which minimizes the complexity under a suitably  ...  We use log(·) to denote the binary logarithm. A.  ... 
doi:10.1109/isit.2014.6875380 dblp:conf/isit/Balatsoukas-StimmingKB14 fatcat:j2iq4fzwsjd6pan4ekg3thd5qu

Improved Successive Cancellation Decoding of Polar Codes

Kai Chen, Kai Niu, Jiaru Lin
2013 IEEE Transactions on Communications  
Unified descriptions of SC, SCL and SCS decoding algorithms are given as path searching procedures on the code tree of polar codes.  ...  codes.  ...  On Different Pruning Ratio τFig. 13 and Fig. 14 give simulations of polar codes with code length N = 1024 code rate R = 0.5 over binary-input additive Gaussian noise channels (BAWGNCs).  ... 
doi:10.1109/tcomm.2013.070213.120789 fatcat:klrh2afexbaankkues6rqmrqw4

Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes [article]

Seyyed Ali Hashemi, Marco Mondelli, Arman Fazeli, Alexander Vardy, John Cioffi, Andrea Goldsmith
2020 arXiv   pre-print
This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints.  ...  and μ is the scaling exponent of the channel.  ...  Furthermore, µ ≈ 3.63 when W is a binary erasure channel (BEC), as shown in [7] , µ ≈ 4 when W is a binary additive white Gaussian noise channel (BAWGNC), as shown in [13] , and it is conjectured that  ... 
arXiv:2012.13378v1 fatcat:v2ty5glqenfpfgdz7icpogsdtm

Reed-Muller Codes: Theory and Algorithms [article]

Emmanuel Abbe and Amir Shpilka and Min Ye
2020 arXiv   pre-print
In particular, the paper discusses the recent connections established between RM codes, thresholds of Boolean functions, polarization theory, hypercontractivity, and the techniques of approximating low  ...  Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science.  ...  that RM codes achieve capacity on erasure channels.  ... 
arXiv:2002.03317v2 fatcat:oaeaq4yyhvdcth3g4djndgfypq

A Split-Reduced Successive Cancellation List Decoder for Polar Codes

Zhaoyang Zhang, Liang Zhang, Xianbin Wang, Caijun Zhong, H. Vincent Poor
2016 IEEE Journal on Selected Areas in Communications  
This paper focuses on low complexity successive cancellation list (SCL) decoding of polar codes.  ...  On the other hand, the incorrect paths are more likely to split at the following stages.  ...  INTRODUCTION Polar codes, first discovered by Arıkan [1] , are the first capacity-achieving codes for binary-input discrete memoryless channels with an explicit and deterministic structure.  ... 
doi:10.1109/jsac.2015.2504321 fatcat:xdefhmuzznccvp5qqir6ymvvme

Polar Codes and Their Quantum-Domain Counterparts

Zunaira Babar, Zeynep B. Kaykac Egilmez, Luping Xiang, Daryus Chandra, Robert G. Maunder, Soon Xin Ng, Lajos Hanzo
2019 IEEE Communications Surveys and Tutorials  
We also extend our discussions to quantum polar codes with an emphasis on the underlying quantum-to-classical isomorphism and the syndrome-based quantum polar codes.  ...  Realizing the significance of polar codes, in this paper we provide a comprehensive survey of polar codes, highlighting the major milestones achieved in the last decade.  ...  Similarly, the capacities of a Binary Symmetric Channel (BSC) or a Binary Erasure Channel (BEC) are specified by their respective channel characteristics, i.e. the cross-over probability of the BSC and  ... 
doi:10.1109/comst.2019.2937923 fatcat:tno37ac5izbljlsf7apqcpapsq

Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability [article]

Hsin-Po Wang, Iwan Duursma
2018 arXiv   pre-print
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels.  ...  :1810.04298] analyzing general codes over general channels.  ...  Polar Codes with Larger Kernels Attacking on General Channels For channels that are not binary, [KSU10] does not apply anymore.  ... 
arXiv:1812.08112v1 fatcat:eobjw5c5k5abxofjfdug4ublse

Complexity and Second Moment of the Mathematical Theory of Communication [article]

Hsin-Po Wang
2021 arXiv   pre-print
The two aforementioned results are built upon two pillars: a versatile framework that generates codes on the basis of channel polarization, and a calculus-probability machinery that evaluates the performances  ...  Over any discrete memoryless channel, I build codes such that: (1) their error probabilities and rates scale like random codes; and (2) their en/decoding complexities scale like polar codes.  ...  They had 0.2669 0.2841 over binary erasure channels (BECs). The upper bound was brought down to 3.553 1 over binary-input discrete-output memoryless channels (BDMCs) [GHU12] .  ... 
arXiv:2107.06420v1 fatcat:q35kl44i45b5xcybodesjaxzwy

Coded noncoherent communication with amplitude/phase modulation: from shannon theory to practical architectures

Noah Jacobsen, Upamanyu Madhow
2008 IEEE Transactions on Communications  
Serial concatenation of a binary outer channel code with an inner differential modulation code provides a turbo structure that, along with the channel memory, is exploited for joint iterative channel and  ...  The transceiver is noncoherent, neither requiring pilots for channel estimation and tracking nor assuming prior channel knowledge on the part of the receiver.  ...  In a typical OFDM system, the channel gain can be well modeled as constant over a time-frequency block whose size depends on the channel coherence time and coherence bandwidth.  ... 
doi:10.1109/tcomm.2008.040684 fatcat:vrp6ezqutfazreeioomqiyldxa

Fast Polar Decoders: Algorithm and Implementation

Gabi Sarkis, Pascal Giard, Alexander Vardy, Claude Thibeault, Warren J. Gross
2014 IEEE Journal on Selected Areas in Communications  
Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction.  ...  We present an algorithm, architecture, and FPGA implementation of a gigabit-per-second polar decoder.  ...  the binary erasure channel (BEC) without resource constraints.  ... 
doi:10.1109/jsac.2014.140514 fatcat:abqxxurpszc3lo5pgxu3djrgme

Sub-linear Time Support Recovery for Compressed Sensing using Sparse-Graph Codes [article]

Xiao Li, Dong Yin, Sameer Pawar, Ramtin Pedarsani, Kannan Ramchandran
2018 arXiv   pre-print
The measurement matrix in our framework is designed based on the well-crafted sparsification through capacity-approaching sparse-graph codes, where the sparse coefficients can be recovered efficiently  ...  The sub-linear measurement cost and run-time can also be achieved with continuous-valued sparse coefficients, with a slight increment in the logarithmic factors.  ...  Therefore in the noisy setting, according to the channel coding theorem, we can encode the binary indexing matrix using good channel codes with N codewords of block length O(log 2 N ) such that it can  ... 
arXiv:1412.7646v2 fatcat:nnumhodqibgr5ccjm7f2ufnrwi

Signal definition and resource management techniques for upcoming communication and broadcasting systems

Charbel Abdel Nour
2020 Zenodo  
The work concerns code design for binary and non-binary codes with simplified decoding algorithms, their association with high order modulations and multiple antennas, the study of high diversity schemes  ...  The first targets devising algorithms for coded modulations. It was the subject of 9 supervised PhDs and one post-doc.  ...  The occurrence of erasure events sets a bound on the coding rate R.  ... 
doi:10.5281/zenodo.4968707 fatcat:d2zvqd5l5vhq7j6li5kwyc65je
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