It is shown that polar coding is able to produce a series of codes that achieve capacity on symmetric binary-input memoryless channels and the latest result in the moderate deviation regime does not imply the scaling exponent regime as a special case.Expand

The core theme is to incorporate polar coding with large, random, dynamic kernels (which boosts the performance to random’s realm), and the putative codes are optimal in the following manner.Expand

As a corollary, a grafted variant of polar coding almost catches up the code rate and error probability of random codes with complexity slightly larger than $N\log N$ over BEC.Expand

A pruned variant of polar coding is proposed for binary erasure channel (BEC) and has the lowest per-bit time complexity among all capacity-achieving codes known to date.Expand

This work establishes a multilinear algebra foundation to assemble $(n, k, d, \alpha, \beta, M)$-ERRCs for all meaningful tuples, and ties the $\alpha/M$-versus-$\beta/M $ trade-off with cascade codes, the best known construction for this trade-offs.Expand

A pruned variant of polar coding is reinvented for all binary erasure channels for small $\varepsilon>0$ codes with block length, code rate, error probability, and encoding and decoding time complexity.Expand

To multiply astronomic matrices using parallel workers subject to straggling, this work recommends interleaving checksums with some fast matrix multiplication algorithms, and proposes probability-wise favorable configurations whose numbers of workers are close to, if not less than, the thresholds of other codes.Expand

In this work, various ways to re-express the infamous product-matrix construction using skew-symmetric matrices, polynomials, symmetric algebras, and exterior alge bras are explored.Expand