A New Upper Bound on the Capacity of a Class of Primitive Relay Channels
| dc.creator | Tandon, Ravi | |
| dc.creator | Ulukus, Sennur | |
| dc.date | 2008-10-04 | |
| dc.date.accessioned | 2026-07-07T10:07:41Z | |
| dc.date.available | 2026-07-07T10:07:41Z | |
| dc.description | We obtain a new upper bound on the capacity of a class of discrete memoryless relay channels. For this class of relay channels, the relay observes an i.i.d. sequence $T$, which is independent of the channel input $X$. The channel is described by a set of probability transition functions $p(y|x,t)$ for all $(x,t,y)\in \mathcal{X}\times \mathcal{T}\times \mathcal{Y}$. Furthermore, a noiseless link of finite capacity $R_{0}$ exists from the relay to the receiver. Although the capacity for these channels is not known in general, the capacity of a subclass of these channels, namely when $T=g(X,Y)$, for some deterministic function $g$, was obtained in [1] and it was shown to be equal to the cut-set bound. Another instance where the capacity was obtained was in [2], where the channel output $Y$ can be written as $Y=X\oplus Z$, where $\oplus$ denotes modulo-$m$ addition, $Z$ is independent of $X$, $|\mathcal{X}|=|\mathcal{Y}|=m$, and $T$ is some stochastic function of $Z$. The compress-and-forward (CAF) achievability scheme [3] was shown to be capacity achieving in both cases. Using our upper bound we recover the capacity results of [1] and [2]. We also obtain the capacity of a class of channels which does not fall into either of the classes studied in [1] and [2]. For this class of channels, CAF scheme is shown to be optimal but capacity is strictly less than the cut-set bound for certain values of $R_{0}$. We also evaluate our outer bound for a particular relay channel with binary multiplicative states and binary additive noise for which the channel is given as $Y=TX+N$. We show that our upper bound is strictly better than the cut-set upper bound for certain values of $R_{0}$ but it lies strictly above the rates yielded by the CAF achievability scheme. | |
| dc.description | To appear in Proceedings of 46th Annual Allerton Conference on Communication, Control and Computing, Sept. 2008 | |
| dc.identifier | https://arxiv.org/abs/0810.0747 | |
| dc.identifier | http://arxiv.org/abs/0810.0747 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170725 | |
| dc.subject | Information Theory | |
| dc.subject | Artificial Intelligence | |
| dc.subject | H.1.1 | |
| dc.title | A New Upper Bound on the Capacity of a Class of Primitive Relay Channels | |
| dc.type | text |