TY - JOUR
T1 - Minimax universal decoding with an erasure option
AU - Merhav, Neri
AU - Feder, Meir
N1 - Funding Information:
Manuscript received April 15, 2006; revised February 19, 2007. This work was supported by the Israel Science Foundation under Grant 223/05. The material in this paper will be presented at the IEEE International Symposium on Information Theory, Nice, France, June 2007. N. Merhav is with the Department of Electrical Engineering, Technion—Israel Institute of Technology, Technion City, Haifa 32000, Israel (e–mail: [email protected]). M. Feder is with the Department of Electrical Engineering—Systems, Tel-Aviv University, Ramat-Aviv 69978, Israel (e-mail: [email protected]). Communicated by G. Kramer, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2007.894695 1Alternatively, the receiver can use the feedback link only to notify the transmitter when it reached a decision regarding the current message (and keep silent at all other times). In network situations, this would not load the network much as it is done only once per each message.
PY - 2007/5
Y1 - 2007/5
N2 - Motivated by applications of rateless coding, decision feedback, and automatic repeat request (ARQ), we study the problem of universal decoding for unknown channels in the presence of an erasure option. Specifically, we harness the competitive minimax methodology developed in earlier studies, in order to derive a universal version of Forney's classical erasure/list decoder, which in the erasure case, optimally trades off between the probability of erasure and the probability of undetected error. The proposed universal erasure decoder guarantees universal achievability of a certain fraction ξ of the optimum error exponents of these probabilities (in a sense to be made precise in the sequel). A single-letter expression for ξ, which depends solely on the coding rate and the Neyman-Pearson threshold (to be defined), is provided. The example of the binary-symmetric channel is studied in full detail, and some conclusions are drawn.
AB - Motivated by applications of rateless coding, decision feedback, and automatic repeat request (ARQ), we study the problem of universal decoding for unknown channels in the presence of an erasure option. Specifically, we harness the competitive minimax methodology developed in earlier studies, in order to derive a universal version of Forney's classical erasure/list decoder, which in the erasure case, optimally trades off between the probability of erasure and the probability of undetected error. The proposed universal erasure decoder guarantees universal achievability of a certain fraction ξ of the optimum error exponents of these probabilities (in a sense to be made precise in the sequel). A single-letter expression for ξ, which depends solely on the coding rate and the Neyman-Pearson threshold (to be defined), is provided. The example of the binary-symmetric channel is studied in full detail, and some conclusions are drawn.
KW - Channel uncertainty
KW - Competitive minimax
KW - Erasure
KW - Error exponent
KW - Generalized likelihod ratio test (GLRT)
KW - Rateless codes
KW - Universal decoding
UR - http://www.scopus.com/inward/record.url?scp=34248326523&partnerID=8YFLogxK
U2 - 10.1109/TIT.2007.894695
DO - 10.1109/TIT.2007.894695
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AN - SCOPUS:34248326523
SN - 0018-9448
VL - 53
SP - 1664
EP - 1675
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 5
ER -