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For lossy image compression systems, we develop an algorithm, iterative refinement, to improve the decoder's reconstruction compared to standard decoding techniques. Specifically, we propose a recurrent neural network approach for…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
Recent coding strategies for deterministic and noisy relay networks are related to the pipelining of block Markov encoding. For deterministic networks, it is shown that pipelined encoding improves encoding delay, as opposed to end-to-end…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
Recently, Martinez-Penas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted…
Spatially coupled, parallel concatenated codes (SC-PCCs) have been shown to approach channel capacity when decoded using optimal iterative methods. However, under complexity constraints such decoding strategies can result in unacceptable…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
This paper deals with two main issues regarding the short polar codes: the potential of FEC-assisted decoding and optimal code concatenation strategies under various design scenarios. Code concatenation and FEC-assisted decoding are…
The rapidly improving performance of modern hardware renders convolutional codes obsolete, and allows for the practical implementation of more sophisticated correction codes such as low density parity check (LDPC) and turbo codes (TC). Both…
Binary turbo product codes (TPCs) are powerful error-correcting codes constructed from short component codes. Traditionally, turbo product decoding passes log likelihood ratios (LLRs) between the component decoders, inherently losing…
Analog error correction codes, by relaxing the source space and the codeword space from discrete fields to continuous fields, present a generalization of digital codes. While linear codes are sufficient for digital codes, they are not for…
Diffusion large language models (dLLMs) generate text through iterative denoising. In commonly adopted parallel decoding schemes, each step confirms only high-confidence positions while remasking the others. By analyzing dLLM denoising…
Deep learning models generalize well to in-distribution data but struggle to generalize compositionally, i.e., to combine a set of learned primitives to solve more complex tasks. In sequence-to-sequence (seq2seq) learning, transformers are…
The aim of this paper is to propose an alternative method to solve a Fault Tolerant Control problem. The model is a linear system affected by a disturbance term: this represents a large class of technological faulty processes. The goal is…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and…