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Polar Code Moderate Deviation: Recovering the Scaling Exponent
TLDR
In 2008 Arikan proposed polar coding [arXiv:0807.3917] which we summarize as follows: (a) From the root channel $W$ synthesize recursively a series of channels $W_N^{(1)},\dotsc,W_ N^{(N)}$. (b) Select sophisticatedly a subset of synthetic channels indexed by $A$ and freeze the remaining synthetic channels. Expand
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Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability
TLDR
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. Expand
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Log-logarithmic Time Pruned Polar Coding
TLDR
A pruned variant of polar coding is proposed for binary erasure channels where the channel tree is pruned by closely looking at the Bhattacharyya parameters. Expand
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Multilinear Algebra for Distributed Storage
TLDR
An $(n, k, d, \alpha, \beta, M)$-ERRC (exact-repair regenerating code) is a collection of $n$ nodes used to store a file. Expand
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Polar Codes' Simplicity, Random Codes' Durability
TLDR
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Expand
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Parity-Checked Strassen Algorithm
TLDR
To multiply astronomic matrices using parallel workers subject to straggling, we recommend interleaving checksums with fast matrix multiplication algorithms. Expand
Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels
TLDR
A pruned variant of polar coding is reinvented for all binary erasure channels. Expand
Congo Bongo
Multilinear Algebra for Minimum Storage Regenerating Codes
TLDR
An (n, k, d, α)-MSR (minimum storage regeneration) code is a set of n nodes used to store a file. Expand