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We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be…
This study proposes \emph{modular arithmetic erasure channels} (MAECs), a novel class of erasure-like channels with an input alphabet that need not be binary. This class contains the binary erasure channel (BEC) and some other known…
Polar codes, discovered by Ar{\i}kan, are the first error-correcting codes with an explicit construction to provably achieve channel capacity, asymptotically. However, their error-correction performance at finite lengths tends to be lower…
Polar codes are the first class of capacity-achieving forward error correction (FEC) codes. They have been selected as one of the coding schemes for the 5G communication systems due to their excellent error correction performance when…
Among error-correcting codes, polar codes are the first to provably achieve channel capacity with an explicit construction. In this work, we present software implementations of a polar decoder that leverage the capabilities of modern…
Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless output-symmetric channel. One of the few drawbacks of the original polar code construction is that it is not universal. This means…
We consider a queue-channel model that captures the waiting time-dependent degradation of information bits as they wait to be transmitted. Such a scenario arises naturally in quantum communications, where quantum bits tend to decohere…
Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for…
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 consider finite-level, symmetric quantization procedures for construction and decoding of polar codes. Whether polarization occurs in the presence of quantization is not known in general. Hassani and Urbanke have shown that a simple…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
We provide $poly\log$ sparse quantum codes for correcting the erasure channel arbitrarily close to the capacity. Specifically, we provide $[[n, k, d]]$ quantum stabilizer codes that correct for the erasure channel arbitrarily close to the…
An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming…
Characterizing the ultimate rates of entanglement distribution is essential for both foundational research and the practical deployment of quantum technologies. To investigate these limits, we introduce an erasure-Pauli channel model…
A multilevel coded modulation scheme is studied that uses solely binary polar codes and Honda-Yamamoto probabilistic shaping. The scheme is shown to achieve the capacity of discrete memoryless channels with input alphabets of cardinality a…
Polar codes are the first codes with a proven capacity-achieving capability, but their decoding faces several challenges, especially under long code lengths. In this paper, we target algorithmic improvements and analyses to enable the…
We consider classical-quantum (cq-)channels with memory, and establish that Ar{\i}kan-constructed polar codes achieve the classical capacity for two key noise models, namely for (i) qubit erasures and (ii) unital qubit noise with channel…
Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of…
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for…
We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present…