TY - GEN

T1 - Polar codes for broadcast channels

AU - Goela, Naveen

AU - Abbe, Emmanuel

AU - Gastpar, Michael

PY - 2013

Y1 - 2013

N2 - Building on polar code constructions proposed by the authors for deterministic broadcast channels, two theorems are introduced in the present paper for noisy two-user broadcast channels. The theorems establish polar code constructions for two important information-theoretic broadcast strategies: (1) Cover's superposition strategy; (2) Marton's construction. One aspect of the polar code constructions is the alignment of polarization indices via constraints placed on the auxiliary and channel-input distributions. The codes achieve capacity-optimal rates for several classes of broadcast channels (e.g., binary-input stochastically degraded channels). Applying Arkan's original matrix kernel for polarization, it is shown that the average probability of error in decoding two private messages at the broadcast receivers decays as O(2 -nβ) where 0 < β < 1/2 and n is the code length. The encoding and decoding complexities remain O(n log n). The error analysis is made possible by defining new polar code ensembles for broadcast channels.

AB - Building on polar code constructions proposed by the authors for deterministic broadcast channels, two theorems are introduced in the present paper for noisy two-user broadcast channels. The theorems establish polar code constructions for two important information-theoretic broadcast strategies: (1) Cover's superposition strategy; (2) Marton's construction. One aspect of the polar code constructions is the alignment of polarization indices via constraints placed on the auxiliary and channel-input distributions. The codes achieve capacity-optimal rates for several classes of broadcast channels (e.g., binary-input stochastically degraded channels). Applying Arkan's original matrix kernel for polarization, it is shown that the average probability of error in decoding two private messages at the broadcast receivers decays as O(2 -nβ) where 0 < β < 1/2 and n is the code length. The encoding and decoding complexities remain O(n log n). The error analysis is made possible by defining new polar code ensembles for broadcast channels.

KW - Cover's superposition codes

KW - Deterministic broadcast channel

KW - Marton's construction

KW - Polar codes

UR - http://www.scopus.com/inward/record.url?scp=84890324319&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890324319&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2013.6620402

DO - 10.1109/ISIT.2013.6620402

M3 - Conference contribution

AN - SCOPUS:84890324319

SN - 9781479904464

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1127

EP - 1131

BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013

T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013

Y2 - 7 July 2013 through 12 July 2013

ER -