TY - GEN

T1 - Exponential source/channel duality

AU - Tridenski, Sergey

AU - Zamir, Ram

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - 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 correct-decoding (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 random-coding 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, settling a long standing conjecture.

AB - 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 correct-decoding (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 random-coding 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, settling a long standing conjecture.

KW - Correct-decoding exponent

KW - Erasure/list decoding

KW - Random coding exponents

KW - Source coding exponents

UR - http://www.scopus.com/inward/record.url?scp=85034066416&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8007108

DO - 10.1109/ISIT.2017.8007108

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AN - SCOPUS:85034066416

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 3140

EP - 3144

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -