Browsing by Subject "Guessing"
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Item Open Access Application of guessing to sequential decoding of polarization-adjusted convolutional (PAC) codes(Institute of Electrical and Electronics Engineers Inc., 2023-08-16) Moradi, MohsenDespite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.Item Open Access Guessing subject to distortion(Institute of Electrical and Electronics Engineers, 1998-05) Arikan, E.; Merhav, N.We investigate the problem of guessing a random vector X within distortion level D. Our aim is to characterize the best attainable performance in the sense of minimizing, in some probabilistic sense, the number of required guesses G(X) until the error falls below D. The underlying motivation is that G(X) is the number of candidate codewords to be examined by a rate-distortion block encoder until a satisfactory codeword is found. In particular, for memoryless sources, we provide a single-letter characterization of the least achievable exponential growth rate of the ρth moment of G(X) as the dimension of the random vector X grows without bound. In this context, we propose an asymptotically optimal guessing scheme that is universal both with respect to the information source and the value of ρ. We then study some properties of the exponent function E(D, ρ) along with its relation to the source-coding exponents. Finally, we provide extensions of our main results to the Gaussian case, guessing with side information, and sources with memory.Item Open Access Hierarchical guessing with a fidelity criterion(Institute of Electrical and Electronics Engineers, 1999) Merhav, N.; Roth, R. M.; Arikan, E.In an earlier paper, we studied the problem of guessing a random vector X within distortion D, and characterized the best attainable exponent E(D, p) of the pth moment of the number of required guesses G(X) until the guessing error falls below D. In this correspondence, we extend these results to a multistage, hierarchical guessing model, which allows for a faster search for a codeword vector at the encoder of a rate-distortion codebook. In the two-stage case of this model, if the target distortion level is D 2, the guesser first makes guesses with respect to (a higher) distortion level D 1, and then, upon his/her first success, directs the subsequent guesses to distortion DI. As in the abovementioned earlier paper, we provide a single-letter characterization of the best attainable guessing exponent, which relies heavily on well-known results on the successive refinement problem. We also relate this guessing exponent function to the source-coding error exponent function of the two-step coding process.Item Open Access The Shannon cipher system with a guessing wiretapper(Institute of Electrical and Electronics Engineers, 1999-09) Merhav, N.; Arikan, E.The Shannon theory of cipher systems is combined with recent work on guessing values of random variables. The security of encryption systems is measured in terms of moments of the number of guesses needed for the wiretapper to uncover the plaintext given the cryptogram. While the encrypter aims at maximizing the guessing effort, the wiretapper strives to minimize it, e.g., by ordering guesses according to descending order of posterior probabilities of plaintexts given the cryptogram. For a memoryless plaintext source and a given key rate, a singleletter characterization is given for the highest achievable guessing exponent function, that is, the exponential rate of the th moment of the number of guesses as a function of the plaintext message length. Moreover, we demonstrate asymptotically optimal strategies for both encryption and guessing, which are universal in the sense of being independent of the statistics of the source. The guessing exponent is then investigated as a function of the key rate and related to the large-deviations guessing performance.