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| Content Provider | IET Digital Library |
|---|---|
| Author | Chong, Zan Kai Goi, Bok Min Ohsaki, Hiroyuki Ng, Bryan Ewe, Hong Tat |
| Abstract | A random code is a rateless erasure code with a generator matrix of randomly distributed binary values. It encodes a message of k symbols into a potentially infinite number of coded symbols. For asymptotically large k, the tail bound in Kolchin's theorem asserts that the high probability of complete decoding (PCD) is attained almost surely with k + 10 coded symbols. However, for small values of k (short messages) it is unclear if such asymptotics are useful. That the random codes achieve a high PCD with k + 10 coded symbols for small k is demonstrated. In particular, a set of lemmas is established and show that the PCD converges to five decimal digits after k = 30. A theorem extending Kolchin's work is formulated and the theorem is used to explain the complete decoding probabilities of random codes in short messages. |
| Starting Page | 251 |
| Ending Page | 253 |
| Page Count | 3 |
| ISSN | 00135194 |
| Volume Number | 51 |
| e-ISSN | 1350911X |
| Issue Number | Issue 3, Feb (2015) |
| Alternate Webpage(s) | https://digital-library.theiet.org/content/journals/el/51/3 |
| Alternate Webpage(s) | https://digital-library.theiet.org/content/journals/10.1049/el.2014.3977 |
| Journal | Electronics Letters |
| Publisher Date | 2015-01-23 |
| Access Restriction | Open |
| Rights Holder | © The Institution of Engineering and Technology |
| Subject Keyword | Code Distributed Binary Values Generator Matrix PCD Probability Probability of Complete Decoding Random Code Statistics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Electrical and Electronic Engineering |
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