Bounded decoders improve error and erasure estimates in short block communication
Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength
Information Theory
Summary
Communicating data in short chunks can lead to different types of problems: sometimes the receiver gets confused and picks the wrong message, and sometimes it just gives up and says it lost the message. The authors show that these two failure types can be separated and accurately bounded using a geometric approach, instead of lumping them together. This helps provide real mathematical support for treating lost messages as erasures in communication protocols. They also explore how often the system mistakenly believes an idle message was sent, which leads to a new simple channel model useful for designing reliable communication systems.
What this means in practice
- •For network protocol designers: Use separate error and erasure probability bounds to better design communication protocols that expect loss rather than confusion in physical layers.
- •For wireless communication engineers: Incorporate the block z-channel abstraction emerging from bounded decoders to reduce false alarms during idle transmissions in noisy wireless links.
Authors
Bin Han, Yao Zhu, Rafael F. Schaefer, Wenwen Chen, Giuseppe Caire, Anke Schmeink, H. Vincent Poor, Hans D. Schotten
Abstract
Block error rate is a standard metric in finite blocklength (FBL) communication, yet it conflates two qualitatively different failure modes: block confusions, where the decoder selects a wrong codeword, and block erasures, where it declares a loss. Higher-layer protocols treat physical-layer failures as erasures, but this cross-layer assumption lacks FBL justification. We derive a rigorous upper bound and a companion lower-side estimate on the block confusion probability (BLCP) and block erasure probability (BLEP) for bounded-distance decoders over additive white Gaussian noise (AWGN) channels at finite blocklength, recasting the coding problem as a geometric sphere packing one. We analyze the sensitivity of these bounds to blocklength and signalto-noise ratio, characterize the envelope of the upper bound, and derive closed-form Chernoff approximations. Extending the model to idle transmission blocks, we bound the false alarm probability (FAP) and show that a block z-channel abstraction emerges from the bounded-decoding geometry. Numerical results confirm that confusion and false alarm probabilities lie far below the error rate constraint, providing quantitative physicallayer support for the block erasure channel and block z-channel abstractions assumed in protocol design.