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Torn-Paper Coding
- Source :
- IEEE Transactions on Information Theory. 67:7904-7913
- Publication Year :
- 2021
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2021.
-
Abstract
- We consider the problem of communicating over a channel that randomly “tears” the message block into small pieces of different sizes and shuffles them. For the binary torn-paper channel with block length $n$ and pieces of length ${\mathrm{ Geometric}}(p_{n})$ , we characterize the capacity as $C = e^{-\alpha }$ , where $\alpha = \lim _{n\to \infty } p_{n} \log n$ . Our results show that the case of ${\mathrm{ Geometric}}(p_{n})$ -length fragments and the case of deterministic length- $(1/p_{n})$ fragments are qualitatively different and, surprisingly, the capacity of the former is larger. Intuitively, this is due to the fact that, in the random fragments case, large fragments are sometimes observed, which boosts the capacity.
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 67
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi...........eb7f63d4e0b4076f692bde9c7efa4082