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We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of…
Redundant code is a persistent challenge in software development that makes systems harder to maintain, scale, and update. It adds unnecessary complexity, hinders bug fixes, and increases technical debt. Despite their impact, removing…
The problem of detecting and removing redundant constraints is fundamental in optimization. We focus on the case of linear programs (LPs), given by $d$ variables with $n$ inequality constraints. A constraint is called \emph{redundant}, if…
In this paper, we present an explicit construction of list-decodable codes for single-deletion and single-substitution with list size two and redundancy 3log n+4, where n is the block length of the code. Our construction has lower…
This paper studies codes that correct bursts of deletions. Namely, a code will be called a $b$-burst-deletion-correcting code if it can correct a deletion of any $b$ consecutive bits. While the lower bound on the redundancy of such codes…
We construct deletion error-correcting codes in the oblivious model, where errors are adversarial but oblivious to the encoder's randomness. Oblivious errors bridge the gap between the adversarial and random error models, and are motivated…
Most memories suffer from both permanent defects and intermittent random errors. The partitioned linear block codes (PLBC) were proposed by Heegard to efficiently mask stuck-at defects and correct random errors. The PLBC have two separate…
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…
We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which…
We investigate the question of whether or not there exists a noncommutative/ quantum extension of a recent (commutative probabilistic) result of Clarke and Barron. They demonstrated that the Jeffreys' invariant prior of Bayesian theory…
In this paper, we present an efficiently encodable and decodable code construction that is capable of correction a burst of deletions of length at most $k$. The redundancy of this code is $\log n + k(k+1)/2\log \log n+c_k$ for some constant…
We study the effects of finite-precision representation of source's probabilities on the efficiency of classic source coding algorithms, such as Shannon, Gilbert-Moore, or arithmetic codes. In particular, we establish the following simple…
For a linear code $C$ of length $n$ with dimension $k$ and minimum distance $d$, it is desirable that the quantity $kd/n$ is large. Given an arbitrary field $\mathbb{F}$, we introduce a novel, but elementary, construction that produces a…
It is now well known that the performance of a linear code $C$ under iterative decoding on a binary erasure channel (and other channels) is determined by the size of the smallest stopping set in the Tanner graph for $C$. Several recent…
Let $L$ be a finite sequence of natural numbers. In Woryna (2017,2018), we derived some interesting properties for the ratio $\rho_{n,L}=|PR_n(L)|/|UD_n(L)|$, where $UD_n(L)$ denotes the set of all codes over an $n$-letter alphabet and with…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
It is known that the empirical spectral distribution of random matrices obtained from linear codes of increasing length converges to the well-known Marchenko-Pastur law, if the Hamming distance of the dual codes is at least 5. In this…
The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming…
We propose a source/channel duality in the exponential regime, where success/failure in source coding parallels error/correctness in channel coding, and a distortion constraint becomes a log-likelihood ratio (LLR) threshold. We establish…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…