On multiple access channels with feedback (Corresp.)

For the binary erasure multiple access channel, van der Meulen showed in his survey paper that the symmetrical rate pair(0.79113,0.79113)is achievable in the ease of feedback. Here we prove that this rate point is on the boundary of the feedback capacity region. Subsequently we apply this result to demonstrate the fact that the feedback capacity region of the product of two multiple access channels can be strictly larger than the (Minkowski)sum Of the feedback capacity regions for the separate channels.     

Reliability function of a band-limited signaling scheme with feedback (Corresp.)

The performance of a band-limited signaling scheme for an additive white Gaussian noise channel with noiseless feedback is presented.     

Linear feedback rate bounds for regressive channels (Corresp.)

This article presents new tighter upper bounds on the rate of Gaussian autoregressive channels with linear feedback. The separation between the upper and lower bounds is small. We havefrac{1}{2} ln left( 1 + rho left( 1+ sum_{k=1}^{m} alpha_{k} x^{- k} right)^{2} right) leq C_{L} leq frac{1}{2} ln left( 1+ rho left( 1+ sum_{k = 1}^{m} alpha_{k} / sqrt{1 + rho} right)^{2} right), mbox{all rho}, whererho = P/N_{0}W, alpha_{l}, cdots, alpha_{m}are regression coefficients,Pis power,Wis bandwidth,N_{0}is the one-sided innovation spectrum, andxis a root of the polynomial(X^{2} - 1)x^{2m} - rho left( x^{m} + sum^{m}_{k=1} alpha_{k} x^{m - k} right)^{2} = 0.It is conjectured that the lower bound is the feedback capacity.     

Analysis of the optimum linear system for the autoregressive forward channel with noiseless feedback (Corresp.)

The autoregressive channel with noiseless feedback is considered whereNtransmissions of real numbers are     

Rate distortion over band-limited feedback channels (Corresp.)

Although linear feedback is by itself sufficient to achieve capacity of an additive Gaussian white noise (AGWN) channel, it can not, in general, achieve the theoretical minimum mean-squared error for analog Gaussian data. This correspondence gives the necessary and sufficient conditions under which this optimum performance can be achieved.     

A feedback decoding scheme for linear convolutional codes (Corresp.)

A decoding scheme, with feedback, for linear convolutional codes is given. The scheme when applied to linear nonsystematic convolutional codes requires no post-decoding processing involving memory to retrieve the information sequences. This implies that no additional errors occur that are due only to the information retrieving process.     

Asymptotic performance of unrestricted polar quantizers (Corresp.)

Unrestricted polar quantizers (UPQ's) were previously introduced to overcome the weak mean-squared error performance of polar coordinate quantizers for the independent bivariate Gaussian source when the number of levels was small (< 3bits /dimension). An asymptotic ntean-squared error analysis of the UPQ's with a general circularly symmetric source is presented. The performance of the UPQ's is shown to be asymptotically within0.17dB of that of the optimum bivariate quantizer. The results are extended to dimensions greater than two. Examples for the independent Gaussian source are included.     

The feedback capacity of degraded broadcast channels (Corresp.)

The fact that the capacity region of the discrete memoryless physically degraded broadcast channel is not increased by feedback is established.     

Asymptotic performance of Dirichlet rotated polar quantizers (Corresp.)

An upper bound to the asymptotic mean-square error performance of optimized rotated polar quantizers is presented for a circularly symmetric random input. This form of quantizer is of interest because it has a scalar implementation and has been shown, for a small number of levels with a Gaussian source, to have much better performance than either the rectangular or polar schemes previously documented.     

An achievable bound for optimal noiseless coding of a random variable (Corresp.)

For a discreteN-valued random variable (Npossibly denumerably infinite) Leung-Yan-Cheong and Cover have given bounds for the minimal expected length of a one-to-one (not necessarily uniquely decodable) codeL_{1:1}=sum_{i=1}^{N} p_{i} log left( frac{1}{2} + 1 right).It is shown that the best possible case occurs for certain denumerably infinite sets of nonzero probabilities. This absolute bound is related to the Shannon entropyHof the distribution by(h (cdot)is the binary entropy function).     

A block code for noiseless asynchronous multiple-access OR channel (Corresp.)

A Mock code for the noiseless multiple access OR channel is introduced. An exponential error bound is proven if the sum of the equal code rates of the asynchronousTusers is less thanln 2.     

On the performance of a nonparametric detection scheme for dependent data (Corresp.)

A nonparametric scheme for detecting a constant signal embedded in m-dependent noise is cousidered, aud the performance of the detector in both the asymptotic case and the case of a finite number of samples is investigated. It is shown that the design of the detector with a finite amount of data can be radically different from the design based upon the asymptotic limit.     

Minimax universal noiseless coding for unifilar and Markov sources (Corresp.)

Constructive upper bounds are presented for minimax universal noiseless coding of unifilar sources without any ergodicity assumptionS. These bounds are obtained by quantizing the estimated probability distribution of source letters with respect to the relative entropy. They apply both to fixed-length to variable-length (FV) and variable-length to fixed-length (VF) codes. Unifilar sources are a generalization of the usual definition of Markov sources, so these results apply to Markov sources as well. These upper bounds agree asymptotically with the lower bounds given by Davisson for FV coding of stationary ergodic Markov sources.     

Asymptotic performance and complexity of a coding scheme for memoryless channels

The purpose of this paper is to show that decoding complexity need not grow exponentially with the code block length at rates close to channel capacity and also to show the expediency of the approach of imbedding codes in each other. It is demonstrated that it is possible to communicate over a memoryless channel of capacityCat any rateR < Cwith a probability of error of less than2^{-E(R)nu}, E(R) > 0, per block of a length approximately proportional tonu^{2}and with a computational decoding complexity per digit which is asymptotically proportional tonu^{alpha}whennuis large,nu^{alpha}being finite forR < C.(alpha rightarrow mbox{as} R rightarrow C, alpha rightarrow 2 mbox{as} R rightarrow 0).     

Sequential decision feedback with a MAP strategy (Corresp.)

A computer simulation technique is used to evaluate the performance of the MAP strategy for sequential block orthogonal signaling over a Gaussian channel with noiseless and delayless feedback. The system performance is given in terms of the character error probability. The obtained results are compared with those derived using other suboptimum strategies previously proposed.     

On noiseless source coding with specified encoder output symbol frequencies (Corresp.)

A method is presented for generating prefix-condition codes in which the relative frequencies of the encoder output symbols are close to a previously specified probability distribution. A Kraft-like inequality is developed for this purpose.     

Asymptotic performance of optimum bit-by-bit decoding for the white Gaussian channel (Corresp.)

Asymptotic expressions are derived for the probability of bit error for optimum bit-by-bit decoding of a linear binary block code for the white Gaussian noise channel.     

Permutation codes for discrete channels (Corresp.)

A class of nonlinear codes for discrete channels is defined with the use of permutation groups. Several examples of such codes are given; their parameters are similar to those for Reed-Solomon codes in some cases. Decoding algorithms are discussed.     

Binary codes for compound channels (Corresp.)

The error correcting capabilities are studied of some binary codes used on channels where both independent and burst errors may occur. The compound distance profile is introduced, and a lower bound on this profile is obtained for a class of modified maximum distance separable codes. Several constructions are presented as an illustration.