Related papers: Modified Rice-Golomb Code for Predictive Coding of…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…
This paper develops an algorithmic approach for obtaining approximate, numerical estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which satisfy a given constraint. Our algorithm is based on a statistical…
Marlin is a Variable-to-Fixed (VF) codec optimized for high decoding speed through the use of small sized dictionaries that fit in the L1 cache of most CPUs. While the size of Marlin dictionaries is adequate for decoding, they are still too…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
Coded distributed computation has become common practice for performing gradient descent on large datasets to mitigate stragglers and other faults. This paper proposes a novel algorithm that encodes the partial derivatives themselves and…
In this paper, techniques for improving multichannel lossless coding are examined. A method is proposed for the simultaneous coding of two or more different renderings (mixes) of the same content. The signal model uses both past samples of…
In the torn paper channel, a transmitted codeword is broken at random locations into fragments that arrive at the decoder in an unordered manner. A central theoretical challenge within this model is global alignment -- the task of…
Distributed algorithms are often beset by the straggler effect, where the slowest compute nodes in the system dictate the overall running time. Coding-theoretic techniques have been recently proposed to mitigate stragglers via algorithmic…
Guessing random additive noise decoding (GRAND) is a recently proposed decoding paradigm particularly suitable for codes with short length and high rate. Among its variants, ordered reliability bits GRAND (ORBGRAND) exploits soft…
The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which…
We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code…
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…
Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order…
We consider $t$-Lee-error-correcting codes of length $n$ over the residue ring $\mathbb{Z}_m := \mathbb{Z}/m\mathbb{Z}$ and determine upper and lower bounds on the number of $t$-Lee-error-correcting codes. We use two different methods,…
MDS codes play a central role in practice due to their broad applications. To date, most known MDS codes are generalized Reed-Solomon (GRS) codes, leaving codes that are not equivalent to GRS codes comparatively less understood. Studying…
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further…
Practical constructions of lossless distributed source codes (for the Slepian-Wolf problem) have been the subject of much investigation in the past decade. In particular, near-capacity achieving code designs based on LDPC codes have been…
Most implementations of sampling algorithms for continuous distributions use floating-point numbers, which introduce round-off errors and approximations. These errors can be difficult to analyze, and can cause security issues when used in…
Recently the sparse representation based classification (SRC) has been proposed for robust face recognition (FR). In SRC, the testing image is coded as a sparse linear combination of the training samples, and the representation fidelity is…
Error correction techniques traditionally focus on the co-design of restricted code-structures in tandem with code-specific decoders that are computationally efficient when decoding long codes in hardware. Modern applications are, however,…