Simplified Erasure/List Decoding

Weinberger, Nir; Merhav, Neri

doi:10.1109/tit.2017.2689778

Cited by 8 publications

(9 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As was recently demonstrated in [22], while φ L and φ H are much simpler to implement than φ ′ , they have the potential to cause only slight loss in exponents compared to φ ′ . Since the random coding performance of φ H is simply obtained by the standard analysis of hypothesis testing between two memoryless hypotheses (cf.…”

Section: B Simplified Detectors/decodersmentioning

confidence: 95%

“…In light of (22), this implies that φ ′ satisfies the MD and FA constraints, and at the same time, achieves an IE exponent at least as large as that of φ * .…”

Section: Proposition 3 For Any Given Sequence Of Codesmentioning

confidence: 97%

“…This is in sharp contrast to ordinary decoders, based on comparison of single likelihood terms which can be carried out in the logarithmic scale, rendering them numerically feasible. In a recent related work [22] dealing with the optimal erasure/list decoder [17], it was observed that a much simplified decoder is asymptotically optimal. For the detector/decoder discussed in this paper, this simplification of (17) implies that the rejection region…”

Section: B Simplified Detectors/decodersmentioning

confidence: 99%

See 2 more Smart Citations

Channel Detection in Coded Communication

Weinberger

Merhav

2017

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to detect the set which contains the prevailing channel. We begin with the simplified case where each of the sets is a singleton. For any given code, we derive the optimum detection/decoding rule in the sense of the best trade-off among the probabilities of decoding error, false alarm, and misdetection, and also introduce sub-optimal detection/decoding rules which are simpler to implement. Then, various achievable bounds on the error exponents are derived, including the exact single-letter characterization of the random coding exponents for the optimal detector/decoder. We then extend the random coding analysis to general sets of channels, and show that there exists a universal detector/decoder which performs asymptotically as well as the optimal detector/decoder, when tuned to detect a channel from a specific pair of channels. The case of a pair of binary symmetric channels is discussed in detail.

show abstract

Section: B Simplified Detectors/decodersmentioning

confidence: 95%

“…In light of (22), this implies that φ ′ satisfies the MD and FA constraints, and at the same time, achieves an IE exponent at least as large as that of φ * .…”

Section: Proposition 3 For Any Given Sequence Of Codesmentioning

confidence: 97%

Section: B Simplified Detectors/decodersmentioning

confidence: 99%

See 1 more Smart Citation

Channel Detection in Coded Communication

Weinberger

Merhav

2017

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, Huleihel et al [14] showed that the random coding exponent for erasure decoding is not universally achievable and established a simple relation between the total and undetected error exponents. Weinberger and Merhav [15] analyzed a simplified decoder for erasure decoding. Hayashi and Tan [16] derived ensembletight moderate deviations and second-order results for erasure decoding over additive DMCs.…”

Section: A Background and Related Workmentioning

confidence: 99%

Exact Error and Erasure Exponents for the Asymmetric Broadcast Channel

Cao

Tan

2018

2018 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

Consider the asymmetric broadcast channel with a random superposition codebook, which may be comprised of constant composition or i.i.d. codewords. By applying Forney's optimal decoder for individual messages and the message pair for the receiver that decodes both messages, exact (ensembletight) error and erasure exponents are derived. It is shown that the optimal decoder designed to decode the pair of messages achieves the optimal trade-off between the total and undetected exponents associated with the optimal decoder for the private message. Convex optimization-based procedures to evaluate the exponents efficiently are proposed. Finally, numerical examples are presented to illustrate the results.

show abstract

“…The fixed composition version of the random coding error exponent for the simplified decoder was derived recently in [10]. In comparison, the i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Exponential source/channel duality

Tridenski

Zamir

2017

2017 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

Abstract-We propose a source/channel duality in the exponential regime, where success/failure in source coding parallels error/correctness in channel coding, and a distortion constraint becomes a log-likelihood ratio (LLR) threshold. We establish this duality by first deriving exact exponents for lossy coding of a memoryless source P , at distortion D, for a general i.i.d. codebook distribution Q, for both encoding success (R < R(P, Q, D)) and failure (R > R(P, Q, D)). We then turn to maximum likelihood (ML) decoding over a memoryless channel P with an i.i.d. input Q, and show that if we substitute P = QP , Q = Q, and D = 0 under the LLR distortion measure, then the exact exponents for decoding-error (R < I(Q, P )) and strict correctdecoding (R > I(Q, P )) follow as special cases of the exponents for source encoding success/failure, respectively. Moreover, by letting the threshold D take general values, the exact randomcoding exponents for erasure (D > 0) and list decoding (D < 0) under the simplified Forney decoder are obtained. Finally, we derive the exact random-coding exponent for Forney's optimum tradeoff erasure/list decoder, and show that at the erasure regime it coincides with Forney's lower bound and with the simplified decoder exponent. 1Index Terms-erasure/list decoding, random coding exponents, correct-decoding exponent, source coding exponents.

show abstract

Simplified Erasure/List Decoding

Cited by 8 publications

References 19 publications

Channel Detection in Coded Communication

Channel Detection in Coded Communication

Exact Error and Erasure Exponents for the Asymmetric Broadcast Channel

Exponential source/channel duality

Contact Info

Product

Resources

About