Browsing by Subject "Erasure channels"

Now showing 1 - 4 of 4

Open Access
Broadcast erasure channel with feedback: The two multicast case-Algorithms and bounds
(IEEE, 2013) Onaran, Efe; Gatzianas, M.; Fragouli, C.
We consider the single hop broadcast packet erasure channel (BPEC) with two multicast sessions (each of them destined to a different group of N users) and regularly available instantaneous receiver ACK/NACK feedback. Using the insight gained from recent work on BPEC with unicast and degraded messages [1], [2], we propose a virtual queue based session-mixing algorithm, which does not require knowledge of channel statistics and achieves capacity for N = 2 and iid erasures. Since the extension of this algorithm to N > 2 is not straightforward, we describe a simple algorithm which outperforms standard timesharing for arbitrary N and is actually asymptotically better than timesharing, for any finite N, as the erasure probability goes to zero. We finally provide, through an information-theoretic analysis, sufficient but not necessary asymptotic conditions between N and n (the number of transmissions) for which the achieved sum rate, under any coding scheme, is essentially identical to that of timesharing. © 2013 IEEE.
Open Access
Polar compressive sampling: A novel technique using polar codes
(IEEE, 2010) Pilancı, Mert; Arıkan, Orhan; Arıkan, Erdal
Recently introduced Polar coding is the first practical coding technique that can be proven to achieve the Shannon capacity for a multitude of communication channels. Polar codes are close to Reed-Muller codes except the fact that they are tuned for the parameters of the channel. Hence, Polar codes are shown to offer better performance, e.g., in the erasure channel. It is known that second order Reed-Muller codes can be used for Compressed Sensing. Inspired by that result, we propose Polar codes as measurement matrices in CS and compare their numerical performances. We also present the algebraic relation between the erasure channel and CS theory, and discuss fast solution techniques. ©2010 IEEE.
Open Access
Unitary precoding and basis dependency of MMSE performance for gaussian erasure channels
(IEEE, 2014) Özçelikkale, A.; Yüksel S.; Özaktaş, Haldun M.
We consider the transmission of a Gaussian vector source over a multidimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the minimum mean-square error (MMSE) performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions for a class of settings are presented. For random sampling of signals that have a low number of degrees of freedom, we present MMSE bounds that hold with high probability. Our results illustrate how the spread of the eigenvalue distribution and the unitary transformation contribute to these performance guarantees. The performance of the discrete Fourier transform (DFT) is also investigated. As a benchmark, we investigate the equidistant sampling of circularly wide-sense stationary signals, and present the explicit error expression that quantifies the effects of the sampling rate and the eigenvalue distribution of the covariance matrix of the signal. These findings may be useful in understanding the geometric dependence of signal uncertainty in a stochastic process. In particular, unlike information theoretic measures such as entropy, we highlight the basis dependence of uncertainty in a signal with another perspective. The unitary encoding space restriction exhibits the most and least favorable signal bases for estimation. © 2014 IEEE.
Open Access
An upper bound on the capacity of non-binary deletion channels
(IEEE, 2013) Rahmati, M.; Duman, Tolga M.
We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser in [1] are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability d, denoted by C2K(d), and the capacity of the binary deletion channel with the same deletion probability, C2(d), that is, C2K(d) ≤ C2(d)+(1-d) log(K). Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as d → 0. © 2013 IEEE.