Abstract: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 d… Show more
“…where ( 10) is equivalent to (7) since |t| + = max {0, t}. In [7] the inner minimum of ( 8) was used as a basis of an iterative procedure to find minimizing solutions of (7).…”
Section: Correct-decoding Exponentmentioning
confidence: 99%
“…By a similar method, we also show convergence of the fixed-slope counterpart of the minimization (5), which is an alternating minimization at fixed ρ, based on the double minimum [10]…”
Section: Introductionmentioning
confidence: 97%
“…Such distribution Q has a practical meaning of a channel input distribution achieving reliable communication. In [7], an iterative minimization procedure for computation of E c (R) at fixed R is proposed, using the property that E c (R) can be written as a double minimum [8]:…”
Section: Introductionmentioning
confidence: 99%
“…where the inner min equals sup 0 ≤ ρ < 1 E 0 (−ρ, Q) + ρR . In [7], the inner minimum of ( 5) is computed stochastically by virtue of a correct-decoding event itself, yielding the minimizing solution T * V * . The computation is then repeated iteratively, by assigning Theorem 1], that the iterative procedure using the inner minimum of (5) leads to convergence of this minimum to the double minimum (5), which is evaluated at least over some subset of the support of the initial distribution Q 0 .…”
Section: Introductionmentioning
confidence: 99%
“…In the current work, we improve the result of [7]. We modify the method of Csiszár and Tusnády [9] to prove that the iterative minimization procedure of [7] converges to the global minimum (5) over the support of the initial distribution Q 0 itself, for any R (i.e., not only to E c (R) = 0), and without any additional condition.…”
For a discrete memoryless channel with finite input and output alphabets, we prove convergence of iterative computation of the optimal correct-decoding exponent as a function of communication rate, for a fixed rate and for a fixed slope.
“…where ( 10) is equivalent to (7) since |t| + = max {0, t}. In [7] the inner minimum of ( 8) was used as a basis of an iterative procedure to find minimizing solutions of (7).…”
Section: Correct-decoding Exponentmentioning
confidence: 99%
“…By a similar method, we also show convergence of the fixed-slope counterpart of the minimization (5), which is an alternating minimization at fixed ρ, based on the double minimum [10]…”
Section: Introductionmentioning
confidence: 97%
“…Such distribution Q has a practical meaning of a channel input distribution achieving reliable communication. In [7], an iterative minimization procedure for computation of E c (R) at fixed R is proposed, using the property that E c (R) can be written as a double minimum [8]:…”
Section: Introductionmentioning
confidence: 99%
“…where the inner min equals sup 0 ≤ ρ < 1 E 0 (−ρ, Q) + ρR . In [7], the inner minimum of ( 5) is computed stochastically by virtue of a correct-decoding event itself, yielding the minimizing solution T * V * . The computation is then repeated iteratively, by assigning Theorem 1], that the iterative procedure using the inner minimum of (5) leads to convergence of this minimum to the double minimum (5), which is evaluated at least over some subset of the support of the initial distribution Q 0 .…”
Section: Introductionmentioning
confidence: 99%
“…In the current work, we improve the result of [7]. We modify the method of Csiszár and Tusnády [9] to prove that the iterative minimization procedure of [7] converges to the global minimum (5) over the support of the initial distribution Q 0 itself, for any R (i.e., not only to E c (R) = 0), and without any additional condition.…”
For a discrete memoryless channel with finite input and output alphabets, we prove convergence of iterative computation of the optimal correct-decoding exponent as a function of communication rate, for a fixed rate and for a fixed slope.
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