Correlations Between the Synthetic Channels in Polar Codes
Event details
| Date | 15.07.2019 |
| Hour | 14:00 › 16:00 |
| Speaker | Yunus Inan |
| Location | |
| Category | Conferences - Seminars |
EDIC candidacy exam
Exam president: Prof. Michael Gastpar
Thesis advisor: Prof. Emre Telatar
Co-examiner: Dr. Nicolas Macris
Abstract
Polar coding is a constructive method invented by
Arikan [1], which achieves the symmetric capacity of binary-input
discrete memoryless channels (B-DMC). First, we summarize
Arikan’s seminal paper. Then, some of the code construction
methods for polar codes [1], [2] are investigated. Lastly, we
address the question of block error probability under successive
cancellation decoder (SCD) being asymptotically tight with respect
to the union bound. In [3], the authors have shown this is
indeed true for binary erasure channels (BEC) by tracking the joint channel events with a correlation
metric. However, the asymptotic behavior is still unknown in
general since the output alphabet grows exponentially in block
length and it not possible to track all events. We propose some
methods that may help to resolve this problem by combining the
two approaches in [3] and [2], that is, tracking the joint channel
events with a suitable correlation metric while keeping the output
alphabet constant.
Background papers
Channel polarization: A method for constructing capacity achieving codes for symmetric binary-input memoryless channels, by E. Arikan, in
IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051–3073, July, 2009.
How to construct polar codes, by I. Tal and A. Vardy, in IEEE Transactions on Information Theory, vol. 59, no. 10, pp. 6562–6582, Oct 2013.
On the correlation between polarized becs, by M. B. Parizi and E. Telatar, in 2013 IEEE International Symposium on Information Theory, July 2013, pp. 784–788.
Exam president: Prof. Michael Gastpar
Thesis advisor: Prof. Emre Telatar
Co-examiner: Dr. Nicolas Macris
Abstract
Polar coding is a constructive method invented by
Arikan [1], which achieves the symmetric capacity of binary-input
discrete memoryless channels (B-DMC). First, we summarize
Arikan’s seminal paper. Then, some of the code construction
methods for polar codes [1], [2] are investigated. Lastly, we
address the question of block error probability under successive
cancellation decoder (SCD) being asymptotically tight with respect
to the union bound. In [3], the authors have shown this is
indeed true for binary erasure channels (BEC) by tracking the joint channel events with a correlation
metric. However, the asymptotic behavior is still unknown in
general since the output alphabet grows exponentially in block
length and it not possible to track all events. We propose some
methods that may help to resolve this problem by combining the
two approaches in [3] and [2], that is, tracking the joint channel
events with a suitable correlation metric while keeping the output
alphabet constant.
Background papers
Channel polarization: A method for constructing capacity achieving codes for symmetric binary-input memoryless channels, by E. Arikan, in
IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051–3073, July, 2009.
How to construct polar codes, by I. Tal and A. Vardy, in IEEE Transactions on Information Theory, vol. 59, no. 10, pp. 6562–6582, Oct 2013.
On the correlation between polarized becs, by M. B. Parizi and E. Telatar, in 2013 IEEE International Symposium on Information Theory, July 2013, pp. 784–788.
Practical information
- General public
- Free