Related papers: Polar Coded Computing: The Role of the Scaling Exp…
We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
We introduce an error resilient distributed computing method based on an extension of the channel polarization phenomenon to distributed algorithms. The method leverages an algorithmic split operation that transforms two identical compute…
Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel…
Systematic polar codes are shown to outperform non-systematic polar codes in terms of the bit-error-rate (BER) performance. However theoretically the mechanism behind the better performance of systematic polar codes is not yet clear. In…
This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief…
Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially-coupled…
Improved bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is…
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the…
We consider the problem of determining the trade-off between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters…
The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes…
We study the performance of generalized polar (GP) codes when they are used for coding schemes involving erasure. GP codes are a family of codes which contains, among others, the standard polar codes of Ar{\i}kan and Reed-Muller codes. We…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
Coded computation is a framework which provides redundancy in distributed computing systems to speed up largescale tasks. Although most existing works assume an error-free scenarios in a master-worker setup, the link failures are common in…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
Polarization is an unprecedented coding technique in that it not only achieves channel capacity, but also does so at a faster speed of convergence than any other coding technique. This speed is measured by the ``scaling exponent'' and its…
Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the analysis and construction of polar codes involve the complex iterative-calculation. In…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
Polar codes that approach capacity at a near-optimal speed, namely with scaling exponents close to $2$, have been shown possible for $q$-ary erasure channels (Pfister and Urbanke), the BEC (Fazeli, Hassani, Mondelli, and Vardy), all BMS…
Transmission of information reliably and efficiently across channels is one of the fundamental goals of coding and information theory. In this respect, efficiently decodable deterministic coding schemes which achieve capacity provably have…