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An extension of the order bound for AG codes
TLDR
The most successful method to obtain lower bounds for the minimum distance of an algebraic geometric code is the order bound, which generalizes the Feng-Rao bound. Expand
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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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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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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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Isometry-dual flags of AG codes
TLDR
A complete flag of codes is isometry-dual if the dual of the flag is the image of the original flag under an isometry. 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
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