Related papers: Error exponents of typical random codes
Random jammers that overpower transmitted signals are a practical concern for many wireless communication protocols. As such, wireless receivers must be able to cope with standard channel noise and jamming (intentional or unintentional). To…
When information is to be transmitted over an unknown, possibly unreliable channel, an erasure option at the decoder is desirable. Using constant-composition random codes, we propose a generalization of Csiszar and Korner's Maximum Mutual…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Storage systems have a strong need for substantially improving their error correction capabilities, especially for long-term storage where the accumulating errors can exceed the decoding threshold of error-correcting codes (ECCs). In this…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
Solving Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions. However, few work about global error estimation can be…
We analyze random coding error exponents associated with erasure/list Slepian-Wolf decoding using two different methods and then compare the resulting bounds. The first method follows the well known techniques of Gallager and Forney and the…
We consider data transmission across discrete memoryless channels (DMCs) using variable-length codes with feedback. We consider the family of such codes whose rates are $\rho_N$ below the channel capacity $C$, where $\rho_N$ is a positive…
Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and…
Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be…
It is well known that the minimum distance for linear network codes plays the same role as the minimum distance for classical error control codes. However, Yang and Yeung (2008) discovered that for nonlinear network codes, the minimum…
In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of supervised machine learning algorithms is introduced. The method relies on the notion of…
Rank metric codes and constant-dimension codes (CDCs) have been considered for error control in random network coding. Since decoder errors are more detrimental to system performance than decoder failures, in this paper we investigate the…
Large Language Models (LLMs) have demonstrated unprecedented capabilities in code generation. However, there remains a limited understanding of code generation errors that LLMs can produce. To bridge the gap, we conducted an in-depth…
DNA, with remarkable properties of high density, durability, and replicability, is one of the most appealing storage media. Emerging DNA storage technologies use composite DNA letters, where information is represented by probability…
This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with…
We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel (BSC)…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…
We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function…