arXiv subjects

Helmut Boelcskei

Publications and source records attributed to Helmut Boelcskei.

4 recordsLinked to original sources

arXiv2024

Algorithmic complexity of $\beta$-expansions and application to A/D conversion

We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and $\beta$-expansions. These relationships allow to develop intuitions on the complexity behavior of $\beta$-expansions, and raise problems related to compressibility of binary sequences generated in the context of A/D conversion relying on $\beta$-expansions. Our last contribution is to solve these problems.

cs.IT↗

arXiv2009

Interference Alignment with Limited Feedback

We consider single-antenna interference networks where M sources, each with an average transmit power of P/M, communicate with M destinations over frequency-selective channels (with L taps each) and each destination has perfect knowledge of its channels from each of the sources. Assuming that there exist error-free non-interfering broadcast feedback links from each destination to all the nodes (i.e., sources and destinations) in the network, we show that naive interference alignment, in conjunction with vector quantization of the impulse response coefficients according to the scheme proposed in Mukkavilli et al., IEEE Trans. IT, 2003, achieves full spatial multiplexing gain of M/2, provided that the number of feedback bits broadcast by each destination is at least M(L-1) log P.

cs.IT↗

arXiv2009

Diversity-Multiplexing Tradeoff in Fading Interference Channels

We analyze two-user single-antenna fading interference channels with perfect receive channel state information (CSI) and no transmit CSI. We compute the diversity-multiplexing tradeoff (DMT) region of a fixed-power-split Han and Kobayashi (HK)-type superposition coding scheme and provide design criteria for the corresponding superposition codes. We demonstrate that this scheme is DMT-optimal under moderate, strong, and very strong interference by showing that it achieves a DMT outer bound that we derive. Further, under very strong interference, we show that a joint decoder is DMT-optimal and "decouples" the fading interference channel, i.e., from a DMT perspective, it is possible to transmit as if the interfering user were not present. In addition, we show that, under very strong interference, decoding interference while treating the intended signal as noise, subtracting the result out, and then decoding the desired signal, a process known as "stripping", achieves the optimal DMT region. Our proofs are constructive in the sense that code design criteria for achieving DMT-optimality (in the cases where we can demonstrate it) are provided.

cs.IT↗

arXiv2007

Crystallization in large wireless networks

We analyze fading interference relay networks where M single-antenna source-destination terminal pairs communicate concurrently and in the same frequency band through a set of K single-antenna relays using half-duplex two-hop relaying. Assuming that the relays have channel state information (CSI), it is shown that in the large-M limit, provided K grows fast enough as a function of M, the network "decouples" in the sense that the individual source-destination terminal pair capacities are strictly positive. The corresponding required rate of growth of K as a function of M is found to be sufficient to also make the individual source-destination fading links converge to nonfading links. We say that the network "crystallizes" as it breaks up into a set of effectively isolated "wires in the air". A large-deviations analysis is performed to characterize the "crystallization" rate, i.e., the rate (as a function of M,K) at which the decoupled links converge to nonfading links. In the course of this analysis, we develop a new technique for characterizing the large-deviations behavior of certain sums of dependent random variables. For the case of no CSI at the relay level, assuming amplify-and-forward relaying, we compute the per source-destination terminal pair capacity for M,K converging to infinity, with K/M staying fixed, using tools from large random matrix theory.

cs.IT↗