Channel Reliability Research Articles

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.

Reliability of quantum-mechanical communication systems

We are concerned with the detection of a set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> messages that are transmitted over a channel disturbed by chaotic thermal noise when quantum effects in the communication systems are taken into account. Our attention is restricted to the special case in which the density operators specifying the state of the received field are commutative. In particular, the performance of two special communication systems is evaluated. For a system in which orthogonal signals with known amplitudes and random phases are transmitted over an additive white Gaussian channel, the structure of an optimum receiver is found. Expressions for the system reliability function and channel capacity are derived. For a system in which orthogonal signals are transmitted over a Rayleigh fading channel, the optimum performance is obtained. The optimum degree of diversity for an equal-strength diversity system is found numerically as a function of the average thermal-noise energy and information rate.

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

Optimum Routes in Communication Systems with Channel Capacities and Channel Reliabilities

Given a communication system in which there is associated with each channel a channel capacity and a channel reliability, algorithms are developed for finding routes between a given pair of stations, with maximum capacity and with reliability not less than some prescribed minimum value.

A technique for improving the transmission reliability of a fading channel

Summary form only. An abstract of the above-titled article, taken from the 1963 IEEE International Convention (held March 25-28, New York, NY, USA), is presented.

A note on error detection in noisy logical computers

A method of error detection is proposed for noisy logical computer elements. The proposal extends the range of the propositional variables so that residue class check symbols may be used in error detection. The principal consequence is that individual logical elements may be designed to process binary inputs with arbitrary reliability and nonzero channel capacity.