The Expurgated Error Exponent is Not Universally Achievable
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915827971784704 |
|---|---|
| author | Moeini, Seyed AmirPouya Dalai, Marco Fàbregas, Albert Guillén i |
| author_facet | Moeini, Seyed AmirPouya Dalai, Marco Fàbregas, Albert Guillén i |
| contents | We study the universal attainability of the expurgated error exponent for discrete memoryless channels (DMCs). While the random-coding exponent is known to be universally attainable via maximum mutual information (MMI) decoding for DMCs, it remains open whether the expurgated exponent can be attained universally. We show that this is not the case in general. Specifically, we construct a family of DMCs for which no single sequence of codes can attain the expurgated exponent simultaneously for all channels in the family, even at rate zero. In addition, for the same channel family, we show that MMI decoding fails to achieve the expurgated exponent for any channel in the family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01736 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Expurgated Error Exponent is Not Universally Achievable Moeini, Seyed AmirPouya Dalai, Marco Fàbregas, Albert Guillén i Information Theory We study the universal attainability of the expurgated error exponent for discrete memoryless channels (DMCs). While the random-coding exponent is known to be universally attainable via maximum mutual information (MMI) decoding for DMCs, it remains open whether the expurgated exponent can be attained universally. We show that this is not the case in general. Specifically, we construct a family of DMCs for which no single sequence of codes can attain the expurgated exponent simultaneously for all channels in the family, even at rate zero. In addition, for the same channel family, we show that MMI decoding fails to achieve the expurgated exponent for any channel in the family. |
| title | The Expurgated Error Exponent is Not Universally Achievable |
| topic | Information Theory |
| url | https://arxiv.org/abs/2603.01736 |