Reliability Function Of Channel Research Articles

On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for a system which employs the optimal detection rule. We conjecture that the resulting random-coding bound is ensemble-tight, and consequently optimal within the class of quantization-and-binning schemes.

Code spectrum and the reliability function: Gaussian channel

A new approach to upper bounding the channel reliability function using the code spectrum is described. It allows us to treat both the low and high rate cases in a unified way. In particular, previously known upper bounds are improved and a new derivation of the sphere-packing bound is presented.

Code spectrum and the reliability function: Binary symmetric channel

A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat both the low and high rate cases in a unified way. In particular, previously known upper bounds are improved, and a new derivation of the sphere-packing bound is presented.

A note on the Poor-Verdu upper bound for the channel reliability function

In an earlier work, Poor and Verdu (1995) established an upper bound for the reliability function of arbitrary single-user discrete-time channels with memory. They also conjectured that their bound is tight for all coding rates. We demonstrate via a counterexample involving memoryless binary erasure channels (BECs) that the Poor-Verdu upper bound is not tight at low rates. We conclude by examining possible improvements to this bound.

General formulas for the Neyman-Pearson type-II error exponent subject to fixed and exponential type-I error bounds

The general formulas for the Neyman-Pearson type-II error exponent subject to two different type-I error constraints, as indicated in the title of the correspondence, are established. As revealed in the formulas, the type-II error exponents are fully determined by the ultimate statistical characteristic of the normalized log-likelihood ratio evaluated under the null hypothesis distribution. Applications of the general formulas to distributed Neyman-Pearson detection, and the channel reliability function are also demonstrated.

Lower bounds on reliability functions of variable-length nonsystematic convolutional codes for channels with noiseless feedback

A variable-length, nonsystematic, convolutional encoding, and successive-decoding scheme is devised to establish significant improvements in the reliability functions of memoryless channels with noiseless decision feedback. It is shown that, for any but pathological discrete memoryless channels with noiseless feedback, there exists a variable-length convolutional code such that the reliability function of the channel can be bounded below by the channel capacity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> for all transmission rates less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> . By employing a modified version of this scheme, it is also constructively shown that, for an additive-white-Gaussian-noise (AWGN) channel with noiseless feedback it is possible to find a variable-length convolutional code such that the channel reliability function can be bounded below by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\alpha_0 c_{infty}</tex> for all rates less than the channel capacity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{\infty}</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\alpha_0 = max (1, \gamma/2)</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\gamma</tex> is the maximum allowable expected-peak-to-expected-average-power ratio at the transmitter.

Use of orthogonal signaling in sequential decision feedback

Viterbi [Information and Control, 8, 80–92 (1965)] has previously considered the effect of sequential decision feedback on communication over an additive white gaussian noise channel. In particular, he analyzed a suboptimum transmission scheme using M orthogonal signals and obtained an upper bound on the error probability. In the following presentation we propose a different suboptimum system for the same problem and obtain an exact expression for the error probability. The error probability for our suboptimum scheme is always less than that for Viterbi's scheme and in fact shows significant improvement for rates near channel capacity. Figure 1 shows the improvement in terms of the channel reliability function (which is proportional to the negative exponent of the error probability).2