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In most error correction coding (ECC) frameworks, the typical error metric is the bit error rate (BER) which measures the number of bit errors. For this metric, the positions of the bits are not relevant to the decoding, and in many noise…
We prove that the blocklength $n$ of a linear $3$-query locally correctable code (LCC) $\mathcal{L} \colon {\mathbb F}^k \to {\mathbb F}^n$ with distance $\delta$ must be at least $n \geq 2^{\Omega\left(\left(\frac{\delta^2 k}{(|{\mathbb…
In this paper, we focus on the design and analysis of the Analog Fountain Code (AFC) for short packet communications. We first propose a density evolution (DE) based framework, which tracks the evolution of the probability density function…
Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We…
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error…
Speech coding facilitates the transmission of speech over low-bandwidth networks with minimal distortion. Neural-network based speech codecs have recently demonstrated significant improvements in quality over traditional approaches. While…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Traditional link adaptation (LA) schemes in cellular network must be revised for networks beyond the fifth generation (b5G), to guarantee the strict latency and reliability requirements advocated by ultra reliable low latency communications…
For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based…
We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback…
Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing…
In this paper, new techniques are presented to either simplify or improve most existing upper bounds on the maximum-likelihood (ML) decoding performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly,…
We introduce a novel network-adaptive algorithm that is suitable for alleviating network packet losses for low-latency interactive communications between a source and a destination. Our network-adaptive algorithm estimates in real-time the…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
Mission-critical applications require Ultra-Reliable Low Latency (URLLC) wireless connections, where the packet error rate (PER) goes down to $10^{-9}$. Fulfillment of the bold reliability figures becomes meaningful only if it can be…
Nowadays, real-time video communication over the internet through video conferencing applications has become an invaluable tool in everyone's professional and personal life. This trend underlines the need for video coding algorithms that…