We show that a recursive cost-constrained random coding scheme attains an error exponent that is at least as high as both the random-coding exponent and the expurgated exponent. The random coding scheme enforces that every pair of codewords in the codebook meets a minimum distance condition, and is reminiscent of the Gilbert-Varshamov construction, but with the notable feature of permitting continuous-alphabet channels. The distance function is initially arbitrary, and it is shown that the Chernoff/Bhattacharrya distance suffices to attain the random coding and expurgated exponents.
|Title of host publication||2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - Jul 2019|
|Event||2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France|
Duration: 7 Jul 2019 → 12 Jul 2019
|Name||IEEE International Symposium on Information Theory - Proceedings|
|Conference||2019 IEEE International Symposium on Information Theory, ISIT 2019|
|Period||7/07/19 → 12/07/19|
Bibliographical noteFunding Information:
This work was supported in part by the Israel Science Foundation under grant 631/17, the European Research Council under Grant 725411, by the Spanish Ministry of Economy and Competitiveness under Grant TEC2016-78434-C3-1-R, and by an NUS Early Career Research Award.
© 2019 IEEE.