Everything about Error exponent
Concept in computing
In information theory, the error exponent of a channel code or source code over the block length of the code is the rate at which the error probability decays exponentially with the block length of the code. Formally, it is defined as the limiting ratio of the negative logarithm of the error probability to the block length of the code for large block lengths. For example, if the probability of error of a decoder drops as, where is the block length, the error exponent is. In this example, approaches for large. Many of the information-theoretic theorems are of asymptotic nature, for example, the channel coding theorem states that for any rate less than the channel capacity, the probability of the error of the channel code can be made to go to zero as the block length goes to infinity. In practical situations, there are limitations to the delay of the communication and the block length must be finite. Therefore, it is important to study how the probability of error drops as the block length go to infinity. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Error exponentA 5-minute orientation
- Skim a recent paper: Rate and Detection-Error Exponent Tradeoff for Joint Communication and Sensing of Fixed Channel StatesInfluential work since 2022
- Pick up a classic book: Data structures and algorithm analysis in CThe most-reprinted book on the subject
- Read the landmark paper: Capacity and error exponent for the direct detection photon channel. ICited 176 times
- Go sideways: Shannon's source coding theoremA closely related topic
- Go sideways: Noisy-channel coding theoremA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Capacity and error exponent for the direct detection photon channel. I
Error exponent for source coding with a fidelity criterion
Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors
Capacity and error exponent for the direct detection photon channel. II
The error exponent for the noiseless encoding of finite ergodic Markov sources
On the joint source-channel coding error exponent for discrete memoryless systems
Error Exponent for Multiple-Access Channels: Lower Bounds
On the error exponent of source-channel transmission with a distortion threshold
🆕 Influential since 2022
Rate and Detection-Error Exponent Tradeoff for Joint Communication and Sensing of Fixed Channel States
Error Exponent and Strong Converse for Quantum Soft Covering
Mismatched Binary Hypothesis Testing: Error Exponent Sensitivity
Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent
Reliable Simulation of Quantum Channels: The Error Exponent
📚 Books worth reading
Data structures and algorithm analysis in CMark Allen Weiss · 1993
Discrete mathematicsNorman Biggs · 1985
Introduction to Computing Using PythonLjubomir Perkovic · 2011
Practical Electronics for InventorsPaul Scherz · 2000- 📕Algebra I workbook for dummiesMary Jane Sterling · 2017
The throne of the fisherman built by the carpenter's son, the root, the bond, and the crown of ChristendomT. W. Allies · 1887
The Eucharistic SacrificeMortimer, Alfred G. (Alfred Garnett), 1848-1924, Carter, Thomas Thellusson, 1808-1901 · 1901
Elementary algebraHenry Sinclair Hall · 1895
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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