Related papers: Joint Write-Once-Memory and Error-Control Codes
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Analog computing hardwares, such as Processing-in-memory (PIM) accelerators, have gradually received more attention for accelerating the neural network computations. However, PIM accelerators often suffer from intrinsic noise in the…
Non-orthogonal multiple access (NOMA) schemes have been proved to increase the multiple-access achievable rate with respect to orthogonal multiple access (OMA). In this paper we propose a novel communication system that combines multi-level…
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal…
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…
The polar codes are proven to be capacity-achieving and are shown to have equivalent or even better finite-length performance than the turbo/LDPC codes under some improved decoding algorithms over the additive white Gaussian noise (AWGN)…
In this paper, we propose novel modulation concepts that we call weak composition modulation (WCM) and composition modulation (CM). We use weak and strict compositions of an integer to form codewords of WCM and CM, respectively. For the…
We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded and transmitted over two independent binary memoryless symmetric channels. Each channel capacity is assumed to be characterized by a single…
Polar codes with memory (PCM) are proposed in this paper: a pair of consecutive code blocks containing a controlled number of mutual information bits. The shared mutual information bits of the succeeded block can help the failed block to…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
Universal fault-tolerant quantum computation will require real-time decoding algorithms capable of quickly extracting logical outcomes from the stream of data generated by noisy quantum hardware. We propose modular decoding, an approach…
Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Existing fixed-length feedback communication schemes are either specialized to particular channels (Schalkwijk--Kailath, Horstein), or apply to general channels but either have high coding complexity (block feedback schemes) or are…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless…
We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a…
The channel polarization behavior of polar codes under noise with memory is investigated. By introducing a genie-aided channel model, we first show that the polarized subchannels still converge to extremal channels under the standard polar…