English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In \cite{butman1976} the linear coding scheme is applied, $X_t=g_t\Big(\Theta - {\bf E}\Big\{\Theta\Big|Y^{t-1}, V_0=v_0\Big\}\Big)$,$t=2,\ldots,n$, $X_1=g_1\Theta$, with $\Theta: \Omega \to {\mathbb R}$, aGaussian random variable, to derive a lower bound on the feedback rate, foradditive Gaussian noise (AGN) channels, $Y_t=X_t+V_t, t=1, \ldots, n$, where$V_t$ is a Gaussian autoregressive (AR) noise, and $\kappa \in [0,\infty)$ isthe total transmitter power. For the unit memory AR noise, with parameters $(c,K_W)$, where $c\in [-1,1]$ is the pole and $K_W$ is the variance of theGaussian noise, the lower bound is $C^{L,B} =\frac{1}{2} \log \chi^2$, where$\chi =\lim_{n\longrightarrow \infty} \chi_n$ is the positive root of$\chi^2=1+\Big(1+ \frac{|c|}{\chi}\Big)^2 \frac{\kappa}{K_W}$, and the sequence$\chi_n \triangleq \Big|\frac{g_n}{g_{n-1}}\Big|, n=2, 3, \ldots,$ satisfies acertain recursion, and conjectured that $C^{L,B}$ is the feedback capacity.  In this correspondence, it is observed that the nontrivial lower bound$C^{L,B}=\frac{1}{2} \log \chi^2$ such that $\chi >1$, necessarily implies thescaling coefficients of the feedback code, $g_n$, $n=1,2, \ldots$, growunbounded, in the sense that, $\lim_{n\longrightarrow\infty}|g_n| =+\infty$.The unbounded behaviour of $g_n$ follows from the ratio limit theorem of asequence of real numbers, and it is verified by simulations. It is thenconcluded that such linear codes are not practical, and fragile with respect toa mismatch between the statistics of the mathematical model of the channel andthe real statistics of the channel. In particular, if the error is perturbed by$\epsilon_n>0$ no matter how small, then $X_n =g_t\Big(\Theta - {\bfE}\Big\{\Theta\Big|Y^{t-1}, V_0=v_0\Big\}\Big)+g_n \epsilon_n$, and$|g_n|\epsilon_n \longrightarrow \infty$, as $n \longrightarrow \infty$.

On the Fragile Rates of Linear Feedback Coding Schemes of Gaussian Channels with Memory