Simplified erasure/list decoding

Weinberger, Nir; Merhav, Neri

doi:10.1109/isit.2015.7282851

Cited by 4 publications

(8 citation statements)

References 12 publications

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“…The exponent (8) presents an analog of the error exponent of the Forney simplified decoder [1, eq. 18-20], [12], [13]. Unlike in the case of the simplified decoder [1, eq.…”

Section: A Implicit Expression For the Channel-independent Metricmentioning

confidence: 99%

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Channel Input Adaptation via Natural Type Selection

Tridenski

Zamir

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We consider a channel-independent decoder which is for i.i.d. random codes what the maximum mutualinformation decoder is for constant composition codes. We show that this decoder results in exactly the same i.i.d. random coding error exponent and almost the same correct-decoding exponent for a given codebook distribution as the maximum-likelihood decoder. We propose an algorithm for computation of the optimal correct-decoding exponent which operates on the corresponding expression for the channel-independent decoder. The proposed algorithm comes in two versions: computation at a fixed rate and for a fixed slope. The fixed-slope version of the algorithm presents an alternative to the Arimoto algorithm for computation of the random coding exponent function in the correct-decoding regime. The fixed-rate version of the computation algorithm translates into a stochastic iterative algorithm for adaptation of the i.i.d. codebook distribution to a discrete memoryless channel in the limit of large block length. The adaptation scheme uses i.i.d. random codes with the channel-independent decoder and relies on one bit of feedback per transmitted block. The communication itself is assumed reliable at a constant rate R. In the end of the iterations the resulting codebook distribution guarantees reliable communication for all rates below R + ∆ for some predetermined parameter of decoding confidence ∆ > 0, provided that R + ∆ is less than the channel capacity. Index TermsCorrect-decoding exponent, Arimoto algorithm, Blahut algorithm, unknown channels, input distribution, maximum mutual information, erasure decoder.

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“…The exponent (8) presents an analog of the error exponent of the Forney simplified decoder [1, eq. 18-20], [12], [13]. Unlike in the case of the simplified decoder [1, eq.…”

Section: A Implicit Expression For the Channel-independent Metricmentioning

confidence: 99%

“…The distortion constraint 0 of the lossy encoding can be generalized to an arbitrary threshold, resulting in a family of exponents of the Forney simplified erasure/list decoder for channels [1, eq. 18-20], [12], [13].…”

Section: B Implicit Expressions For the ML Metricmentioning

confidence: 99%

Channel Input Adaptation via Natural Type Selection

Tridenski

Zamir

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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“…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%

“…Therefore, by recalling the definitions of Φ(Q UXY , R 1 , R 2 ) and L 1 (Q XY , R 1 , R 2 , T ) (see (15) and (21)), and combining (117) and (122), we have the exponential equalities (123)-(126) on the top of the next page, 7 where (123) is due to (122) and the fact that ǫ can be made arbitrarily small and (126) is 7 We use the notation . = (i.e., equality to first-order in the exponent) in (123) since the other direction of the inequality in (117) can be derived by replacing iǫ with (i + 1)ǫ in the function E * 3 (·).…”

Section: Proof Of Theoremmentioning

confidence: 99%

Exact Error and Erasure Exponents for the Asymmetric Broadcast Channel

Cao

Tan

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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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.

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“…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)

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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.

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Simplified erasure/list decoding

Cited by 4 publications

References 12 publications

Channel Input Adaptation via Natural Type Selection

Channel Input Adaptation via Natural Type Selection

Exact Error and Erasure Exponents for the Asymmetric Broadcast Channel

Exponential source/channel duality

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