Related papers: Using Pseudocodewords to Transmit Information
Line codes make it possible to mitigate interference, to prevent short pulses, and to generate streams of bipolar signals with no direct-current (DC) power content through balancing. They find application in magnetic recording (MR) devices,…
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…
We propose a method for program generation based on semantic scaffolds, lightweight structures representing the high-level semantic and syntactic composition of a program. By first searching over plausible scaffolds then using these as…
We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we…
One of the primary goals of information theory is to provide limits on the amount of information it is possible to send through various types of communication channels, and to understand the encoding methods that will allow one to achieve…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
Intermediate step methodologies like chain of thoughts (COT) have demonstrated effectiveness in enhancing the performance of Large Language Models (LLMs) on code generation. This study explores the utilization of intermediate languages,…
Pseudoinverses are ubiquitous tools for handling over- and under-determined systems of equations. For computational efficiency, sparse pseudoinverses are desirable. Recently, sparse left and right pseudoinverses were introduced, using…
An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding…
We consider private polynomial computation (PPC) over noncolluding coded databases. In such a setting a user wishes to compute a multivariate polynomial of degree at most $g$ over $f$ variables (or messages) stored in multiple databases…
A novel deep learning method for improving the belief propagation algorithm is proposed. The method generalizes the standard belief propagation algorithm by assigning weights to the edges of the Tanner graph. These edges are then trained…
Motivated by the fact that living cells use molecular circuits (i.e. a set of chemical reactions) for information processing, this paper investigates the problem of designing molecular circuits for demodulation. In our earlier work, we use…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
A new variant of bit interleaved coded modulation (BICM) is proposed. In the new scheme, called Parallel BICM, L identical binary codes are used in parallel using a mapper, a newly proposed finite-length interleaver and a binary dither…
Instruction-tuned large language models (LLMs) excel at many tasks but often fail to use external tools due to complicated and unfamiliar syntax constraints. While extensive fine-tuning and prompting can mitigate the issue, these approaches…
We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order…
Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is…
It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the…
The article explores an encoding and structural information processing approach using sparse bit vectors and fixed-length linear vectors. The following are presented: a discrete method of speculative stochastic dimensionality reduction of…
In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…