Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels
(2010) In IEEE Transactions on Information Theory 56(9). p.4321-4334- Abstract
Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity- achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is shown to be bounded away both from the Gilbert-Varshamov bound (at any rate) and the expurgated exponent (at low rates). The reason for this phenomenon is shown to rely on the symmetry structure of the 8-PSK constellation, which is known to match the cyclic group of order eight, but not the direct product of three copies of the binary group. The... (More)
Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity- achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is shown to be bounded away both from the Gilbert-Varshamov bound (at any rate) and the expurgated exponent (at low rates). The reason for this phenomenon is shown to rely on the symmetry structure of the 8-PSK constellation, which is known to match the cyclic group of order eight, but not the direct product of three copies of the binary group. The presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical-code performance than designing codes whose algebraic structure does not match the channel. This contrasts the well-known fact that the average binary-coset code achieves both the capacity and the random-coding error exponent of any discrete memoryless channel.
(Less)
- author
- Como, Giacomo LU
- organization
- publishing date
- 2010-09
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Coset codes, error exponent, expurgated exponent, Gilbert-Varshamov bound, group codes, linear codes, minimum distance, random codes
- in
- IEEE Transactions on Information Theory
- volume
- 56
- issue
- 9
- article number
- 5550276
- pages
- 14 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:77955740915
- ISSN
- 0018-9448
- DOI
- 10.1109/TIT.2010.2054330
- project
- Modeling and Control of Large Scale Transportation Networks
- language
- English
- LU publication?
- yes
- id
- b567b7b1-1242-4629-a540-cb731af84bf7
- date added to LUP
- 2022-03-22 13:17:34
- date last changed
- 2022-04-26 11:13:59
@article{b567b7b1-1242-4629-a540-cb731af84bf7, abstract = {{<p>Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity- achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is shown to be bounded away both from the Gilbert-Varshamov bound (at any rate) and the expurgated exponent (at low rates). The reason for this phenomenon is shown to rely on the symmetry structure of the 8-PSK constellation, which is known to match the cyclic group of order eight, but not the direct product of three copies of the binary group. The presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical-code performance than designing codes whose algebraic structure does not match the channel. This contrasts the well-known fact that the average binary-coset code achieves both the capacity and the random-coding error exponent of any discrete memoryless channel.</p>}}, author = {{Como, Giacomo}}, issn = {{0018-9448}}, keywords = {{Coset codes; error exponent; expurgated exponent; Gilbert-Varshamov bound; group codes; linear codes; minimum distance; random codes}}, language = {{eng}}, number = {{9}}, pages = {{4321--4334}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Information Theory}}, title = {{Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels}}, url = {{http://dx.doi.org/10.1109/TIT.2010.2054330}}, doi = {{10.1109/TIT.2010.2054330}}, volume = {{56}}, year = {{2010}}, }