Partial strong converse for the non-degraded wiretap channel

We prove the partial strong converse property for the discrete memoryless non-degraded wiretap channel, for which we require the leakage to the eavesdropper to vanish but allow an asymptotic error probability ϵ ∈ [0, 1) to the legitimate receiver. We show that when the transmission rate is above the secrecy capacity, the probability of correct decoding at the legitimate receiver decays to zero exponentially. Therefore, the maximum transmission rate is the same for ϵ ∈ [0, 1), and the partial strong converse property holds. Our work is inspired by a recently developed technique based on information spectrum method and Chernoff-Cramer bound for evaluating the exponent of the probability of correct decoding.

[1]  J. Wolfowitz.  The coding of messages subject to chance errors , 1957 .

[2]  Rudolf Ahlswede,et al.  Multi-way communication channels , 1973 .

[3]  Edward C. van der Meulen,et al.  Random coding theorems for the general discrete memoryless broadcast channel , 1975, IEEE Trans. Inf. Theory.

[4]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[5]  P. Gács,et al.  Bounds on conditional probabilities with applications in multi-user communication , 1976 .

[6]  R. AhlswedC,et al.  Bounds on Conditional Probabilities with Applications in Multi-User Communication , 1976 .

[7]  János Körner,et al.  General broadcast channels with degraded message sets , 1977, IEEE Trans. Inf. Theory.

[8]  Imre Csiszár,et al.  Broadcast channels with confidential messages , 1978, IEEE Trans. Inf. Theory.

[9]  R. Ahlswede.  An elementary proof of the strong converse theorem for the multiple-access channel , 1982 .

[10]  Sergio Verdú,et al.  A general formula for channel capacity , 1994, IEEE Trans. Inf. Theory.

[11]  Hiroki Koga,et al.  Information-Spectrum Methods in Information Theory , 2002 .

[12]  Masahito Hayashi,et al.  Information Spectrum Approach to Second-Order Coding Rate in Channel Coding , 2008, IEEE Transactions on Information Theory.

[13]  H. Vincent Poor,et al.  Channel Coding Rate in the Finite Blocklength Regime , 2010, IEEE Transactions on Information Theory.

[14]  Abbas El Gamal,et al.  Network Information Theory , 2021, 2021 IEEE 3rd International Conference on Advanced Trends in Information Theory (ATIT).

[15]  Matthieu R. Bloch,et al.  Strong Secrecy From Channel Resolvability , 2011, IEEE Transactions on Information Theory.

[16]  Vincent Yan Fu Tan,et al.  Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities , 2014, Found. Trends Commun. Inf. Theory.

[17]  Matthieu R. Bloch,et al.  Information spectrum approach to strong converse theorems for degraded wiretap channels , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[18]  Himanshu Tyagi,et al.  Strong converse for a degraded wiretap channel via active hypothesis testing , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[19]  Information Spectrum Approach to Strong Converse Theorems for Degraded Wiretap Channels , 2015, IEEE Trans. Inf. Forensics Secur..

[20]  Eric Graves,et al.  Equal-image-size source partitioning: Creating strong Fano's inequalities for multi-terminal discrete memoryless channels , 2015, ArXiv.

[21]  Yasutada Oohama.  Strong converse exponent for degraded broadcast channels at rates outside the capacity region , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[22]  Himanshu Tyagi,et al.  Converses For Secret Key Agreement and Secure Computing , 2014, IEEE Transactions on Information Theory.

[23]  Yasutada Oohama.  Strong converse theorems for degraded broadcast channels with feedback , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[24]  Andreas Winter,et al.  “Pretty strong” converse for the private capacity of degraded quantum wiretap channels , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[25]  Yasutada Oohama.  Strong converse for state dependent channels with full state information at the sender and partial state information at the receiver , 2016, 2016 IEEE Information Theory Workshop (ITW).

[26]  Yasutada Oohama.  Exponent Function for Source Coding with Side Information at the Decoder at Rates below the Rate Distortion Function , 2016, ArXiv.

[27]  Yasutada Oohama.  New Strong Converse for Asymmetric Broadcast Channels , 2016, ArXiv.