Title :
The posterior matching feedback scheme: Capacity achieving and error analysis
Author :
Shayevitz, Ofer ; Feder, Meir
Author_Institution :
Dept. of EE-Syst., Tel Aviv Univ., Tel Aviv
Abstract :
Recently, we have introduced a sequential communication scheme for general memoryless channels with feedback based on the idea of posterior matching, providing a unified framework in which the known Horstein and Schalkwijk-Kailath schemes are special cases. In this paper, we show that the posterior matching scheme achieves the mutual information for a large family of channels and input distributions, and provide closed-form expressions for the attainable error probability over a range of rates. Moreover, we derive the achievable rates in a mismatched setting, where the scheme is designed according to the wrong channel model. In particular, our results hold for discrete memoryless channels, thereby confirming a longstanding conjecture that the Horstein scheme achieves capacity. The proof techniques employed utilize novel relations between information rates and convergence properties of iterated function systems.
Keywords :
channel capacity; channel coding; error statistics; iterative methods; maximum likelihood estimation; pattern matching; sequential codes; Horstein schemes; Schalkwijk-Kailath schemes; closed-form expressions; error analysis; error probability; general memoryless channels; iterated function systems; posterior matching feedback scheme; sequential communication scheme; AWGN; Channel capacity; Closed-form solution; Convergence; Error analysis; Error probability; Feedback; Information rates; Memoryless systems; Mutual information;
Conference_Titel :
Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Conference_Location :
Toronto, ON
Print_ISBN :
978-1-4244-2256-2
Electronic_ISBN :
978-1-4244-2257-9
DOI :
10.1109/ISIT.2008.4595117