Upper bound improves error detection limits in communication channels
An Upper Bound to the Undetected Error Exponent with Erasure Decoding at Positive Rates
Information Theory
Summary
When devices send messages, sometimes errors can sneak through without being noticed. The authors studied a way to detect such hidden errors while allowing some messages to be erased when unsure. They found a mathematical limit that tells how well this hidden-error detection can work, especially when messages are sent at rates above zero. Their work improves upon past bounds and shows that the new limit can be tighter in some cases.
What this means in practice
- •For communication system engineers: Design error detection schemes that minimize undetected errors for positive data rates using improved theoretical bounds.
- •For digital signal processing teams: Optimize decoder algorithms with performance limits that identify when erasure decoding helps reduce undetected errors.
Tested on simulated data.
Authors
Seyed AmirPouya Moeini, Marco Dalai, Albert Guillén i Fàbregas
Abstract
We study the undetected-error exponent of discrete memoryless channels with erasure decoding. Assuming that the undetected-error and erasure probabilities vanish, we derive an upper bound on the undetected-error exponent at positive rates. The bound uses Somekh-Baruch's genie-aided argument where an auxiliary output provides the decoder with a list of codewords. It recovers Telatar's tight rate-zero converse and is at least as tight as the straight-line bound. A numerical example shows that the improvement over the straight-line bound can be strict.