On Properties of Rate-Reliability-Distortion Functions

Harutyunyan, Ashot N.; Haroutunian, Evgueni A.

doi:10.1109/tit.2004.836706

Cited by 6 publications

(6 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The idea of analyzing the inverse function of the error exponent was first introduced by Haroutunian et al [9], [10]. They defined the rate-reliability-distortion function as the minimum rate at which the messages of a source can be encoded and then reconstructed by the decoder with an exponentially decreasing probability of error, and proved that the optimal rate-reliability-distortion function is given by (10).…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Computing the optimal exponent of correct decoding for discrete memoryless sources

Jitsumatsu

Oohama

2016

2016 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

The error exponent of fixed-length lossy source coding was established by Marton. Ahlswede showed that this exponent can be discontinuous at a rate R, depending on the probability distribution P of the given information source and the distortion measure d(x, y). The reason for the discontinuity in the error exponent is that there exists (d, ∆) such that the ratedistortion function R(∆|P ) is neither concave nor quasi-concave with respect to P . Arimoto's algorithm for computing the error exponent in lossy source coding is based on Blahut's parametric representation of the error exponent. However, Blahut's parametric representation is a lower convex envelope of Marton's exponent, and the two do not generally agree. The contribution of this paper is to provide a parametric representation that perfectly matches with the inverse function of Marton's exponent, thus avoiding the problem of the rate-distortion function being nonconvex with respect to P . The optimal distribution for fixed parameters can be obtained using Arimoto's algorithm. Performing a nonconvex optimization over the parameters successfully yields the inverse function of Marton's exponent.

show abstract

Section: Resultsmentioning

confidence: 99%

“…3) Minimax theorem: We substitute ( 11) into (10). Then, except for the maximization over ν ≥ 0, we have to evaluate the following saddle point w.r.t.…”

Section: ) a Parametric Expression For The Rate Distortion Functionmentioning

confidence: 99%

Computing the optimal exponent of correct decoding for discrete memoryless sources

Jitsumatsu

Oohama

2016

2016 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

show abstract

“…It turns out (as coming discussion shows) that the described guessing problem is substantially interconnected with the problem of source lossy coding subject to distortion and reliability criteria. The latter, according to [15], as well as further works [14], [19], treats the Shannon rate-distortion coding in view of the error probability exponential decay with exponent E. This implies a more general optimal relation, rate-reliability-distortion one R(P * , E, ∆) between the coding parameters instead of the rate-distortion function R(P * , ∆). For more details, let f c : X N → {1, 2, · · · , C(N)} be an encoding mapping for source N-vectors with C(N) standing for the volume of the code.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Denote by GN (w, P ) a guessing strategy of the wiretapper that for any encryption function guarantees small error probability: e(L(N), GN (w, P ), ∆) ≤ exp{−NE}. Regardless the source probability distribution the optimal guessing strategy under the condition (19) is the key-search attack. The wiretapper can then find the exact x applying description function f −1 N on the key vector and w. Of course it is supposed that guessing of the exact x is also acceptable for the wiretapper.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…By averaging we obtain lower estimate for the expected number of guesses: Granting arbitrariness of ε and ∆ we obtain (8) and (9). It rest to remark that comparison of cases (19) and (20) shows that in condition (19) it is not possible to guess with ∆ = 0 and have smaller number of guesses, because approximate guessing will need more than exp{NR(P, ∆)} guesses, i. e. more than exp{NR K }, which is enough for the exact reconstruction.…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

On the Shannon cipher system with a wiretapper guessing subject to distortion and reliability requirements

Haroutunian

Ghazaryan²

Proceedings IEEE International Symposium on Information Theory,

View full text Add to dashboard Cite

In this paper we discuss the processes in the Shannon cipher system with discrete memoryless source and a guessing wiretapper. The wiretapper observes a cryptogram of Nvector of ciphered messages in the public channel and tries to guess successively the vector of messages within given distortion level ∆ and small probability of error less than exp{−NE} with positive reliability index E. The security of the system is measured by the expected number of guesses which wiretapper needs for the approximate reconstruction of the vector of source messages. The distortion, the reliability criteria and the possibility of upper limiting the number of guesses extend the approach studied by Merhav and Arikan. A single-letter characterization is given for the region of pairs (R L , R) (of the rate R L of the maximum number of guesses L(N) and the rate R of the average number of guesses) in dependence on key rate R K , distortion level ∆ and reliability E.

show abstract

Multiterminal source coding achievable rates and reliability

Haroutunian

1996

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

On Properties of Rate-Reliability-Distortion Functions

Cited by 6 publications

References 7 publications

Computing the optimal exponent of correct decoding for discrete memoryless sources

Computing the optimal exponent of correct decoding for discrete memoryless sources

On the Shannon cipher system with a wiretapper guessing subject to distortion and reliability requirements

Multiterminal source coding achievable rates and reliability

Contact Info

Product

Resources

About