Imperfect Delayed CSIT can be as Useful as Perfect Delayed CSIT: DoF Analysis and Constructions for the BC

In the setting of the two-user broadcast channel, where a two-antenna transmitter communicates information to two single-antenna receivers, recent work by Maddah-Ali and Tse has shown that perfect knowledge of delayed channel state information at the transmitter (perfect delayed CSIT) can be useful, even in the absence of any knowledge of current CSIT. Similar benefits of perfect delayed CSIT were revealed in recent work by Kobayashi et al., Yang et al., and Gou and Jafar, which extended the above to the case of perfect delayed CSIT and imperfect current CSIT. The work here considers the general problem of communicating, over the aforementioned broadcast channel, with imperfect delayed and imperfect current CSIT, and reveals that even substantially degraded and imperfect delayed-CSIT is in fact sufficient to achieve the aforementioned gains previously associated to perfect delayed CSIT. The work proposes novel multi-phase broadcasting schemes that properly utilize knowledge of imperfect delayed and imperfect current CSIT, to match in many cases the optimal degrees-of-freedom (DoF) region achieved with perfect delayed CSIT. In addition to the theoretical limits and explicitly constructed precoders, the work applies towards gaining practical insight as to when it is worth improving CSIT quality.Comment: arXiv admin note: substantial text overlap with arXiv:1205.347

Fundamental Rate-Reliability-Complexity Limits in Outage Limited MIMO Communications

The work establishes fundamental limits with respect to rate, reliability and computational complexity, for a general setting of outage-limited MIMO communications. In the high-SNR regime, the limits are optimized over all encoders, all decoders, and all complexity regulating policies. The work then proceeds to explicitly identify encoder-decoder designs and policies, that meet this optimal tradeoff. In practice, the limits aim to meaningfully quantify different pertinent measures, such as the optimal rate-reliability capabilities per unit complexity and power, the optimal diversity gains per complexity costs, or the optimal number of numerical operations (i.e., flops) per bit. Finally the tradeoff's simple nature, renders it useful for insightful comparison of the rate-reliability-complexity capabilities for different encoders-decoders.Comment: 6 pages, no figures. Slide presentation of partial work at ITA 2010. Published at ISIT201

Full Coded Caching Gains for Cache-less Users

Within the context of coded caching, the work reveals the interesting connection between having multiple transmitters and having heterogeneity in the cache sizes of the receivers. Our work effectively shows that having multiple transmit antennas -- while providing full multiplexing gains -- can also simultaneously completely remove the performance penalties that are typically associated to cache-size unevenness. Focusing on the multiple-input single-output Broadcast Channel, the work first identifies the performance limits of the extreme case where cache-aided users coincide with users that do not have caches, and then expands the analysis to the case where both user groups are cache-aided but with heterogeneous cache-sizes. In the first case, the main contribution is a new algorithm that employs perfect matchings on a bipartite graph to offer full multiplexing as well as full coded-caching gains to both cache-aided as well as cache-less users. An interesting conclusion is that, starting from a single-stream centralized coded caching setting with normalized cache size $\gamma$, then adding $L$ antennas allows for the addition of {up to} approximately $L/\gamma$ extra cache-less users, at no added delay costs. Similarly surprising is the finding that, {beginning} with a single-antenna hybrid system (with both cache-less and cache-aided users), then adding {$L-1$} antennas to the transmitter, as well as endowing the cache-less users with a cumulative normalized cache size $\Gamma_2$, increases the Degrees of Freedom by a \emph{multiplicative} factor of up to $\Gamma_{2}+L$.Comment: 17 pages, partially presented in ITW 2018, Accepted for publication in Transactions on Information Theor

LR-aided MMSE lattice decoding is DMT optimal for all approximately universal codes

Currently for the nt x nr MIMO channel, any explicitly constructed space-time (ST) designs that achieve optimality with respect to the diversity multiplexing tradeoff (DMT) are known to do so only when decoded using maximum likelihood (ML) decoding, which may incur prohibitive decoding complexity. In this paper we prove that MMSE regularized lattice decoding, as well as the computationally efficient lattice reduction (LR) aided MMSE decoder, allows for efficient and DMT optimal decoding of any approximately universal lattice-based code. The result identifies for the first time an explicitly constructed encoder and a computationally efficient decoder that achieve DMT optimality for all multiplexing gains and all channel dimensions. The results hold irrespective of the fading statistics.Comment: 5 pages, submitted to ISIT 0

Wireless Coded Caching: A Topological Perspective

We explore the performance of coded caching in a SISO BC setting where some users have higher link capacities than others. Focusing on a binary and fixed topological model where strong links have a fixed normalized capacity 1, and where weak links have reduced normalized capacity $\tau<1$, we identify --- as a function of the cache size and $\tau$ --- the optimal throughput performance, within a factor of at most 8. The transmission scheme that achieves this performance, employs a simple form of interference enhancement, and exploits the property that weak links attenuate interference, thus allowing for multicasting rates to remain high even when involving weak users. This approach ameliorates the negative effects of uneven topology in multicasting, now allowing all users to achieve the optimal performance associated to $\tau=1$, even if $\tau$ is approximately as low as $\tau\geq 1-(1-w)^g$ where $g$ is the coded-caching gain, and where $w$ is the fraction of users that are weak. This leads to the interesting conclusion that for coded multicasting, the weak users need not bring down the performance of all users, but on the contrary to a certain extent, the strong users can lift the performance of the weak users without any penalties on their own performance. Furthermore for smaller ranges of $\tau$, we also see that achieving the near-optimal performance comes with the advantage that the strong users do not suffer any additional delays compared to the case where $\tau = 1$.Comment: 7 pages, 4 figure

Toward the Performance vs. Feedback Tradeoff for the Two-User MISO Broadcast Channel

For the two-user MISO broadcast channel with imperfect and delayed channel state information at the transmitter (CSIT), the work explores the tradeoff between performance on the one hand, and CSIT timeliness and accuracy on the other hand. The work considers a broad setting where communication takes place in the presence of a random fading process, and in the presence of a feedback process that, at any point in time, may provide CSIT estimates - of some arbitrary accuracy - for any past, current or future channel realization. This feedback quality may fluctuate in time across all ranges of CSIT accuracy and timeliness, ranging from perfectly accurate and instantaneously available estimates, to delayed estimates of minimal accuracy. Under standard assumptions, the work derives the degrees-of-freedom (DoF) region, which is tight for a large range of CSIT quality. This derived DoF region concisely captures the effect of channel correlations, the accuracy of predicted, current, and delayed-CSIT, and generally captures the effect of the quality of CSIT offered at any time, about any channel. The work also introduces novel schemes which - in the context of imperfect and delayed CSIT - employ encoding and decoding with a phase-Markov structure. The results hold for a large class of block and non-block fading channel models, and they unify and extend many prior attempts to capture the effect of imperfect and delayed feedback. This generality also allows for consideration of novel pertinent settings, such as the new periodically evolving feedback setting, where a gradual accumulation of feedback bits progressively improves CSIT as time progresses across a finite coherence period.Comment: Accepted to IEEE Trans. Inf. Theory. This paper was presented in part at the 50th Annual Allerton Conference 2012, at ITA-UCSD 2013, and at ISIT 201

Sphere decoding complexity exponent for decoding full rate codes over the quasi-static MIMO channel

In the setting of quasi-static multiple-input multiple-output (MIMO) channels, we consider the high signal-to-noise ratio (SNR) asymptotic complexity required by the sphere decoding (SD) algorithm for decoding a large class of full rate linear space-time codes. With SD complexity having random fluctuations induced by the random channel, noise and codeword realizations, the introduced SD complexity exponent manages to concisely describe the computational reserves required by the SD algorithm to achieve arbitrarily close to optimal decoding performance. Bounds and exact expressions for the SD complexity exponent are obtained for the decoding of large families of codes with arbitrary performance characteristics. For the particular example of decoding the recently introduced threaded cyclic division algebra (CDA) based codes -- the only currently known explicit designs that are uniformly optimal with respect to the diversity multiplexing tradeoff (DMT) -- the SD complexity exponent is shown to take a particularly concise form as a non-monotonic function of the multiplexing gain. To date, the SD complexity exponent also describes the minimum known complexity of any decoder that can provably achieve a gap to maximum likelihood (ML) performance which vanishes in the high SNR limit.Comment: 19 Pages, 4 figures. Submitted to the IEEE Transactions on Information Theor

Fundamental Limits of Cache-Aided Wireless BC: Interplay of Coded-Caching and CSIT Feedback

Building on the recent coded-caching breakthrough by Maddah-Ali and Niesen, the work here considers the $K$-user cache-aided wireless multi-antenna (MISO) symmetric broadcast channel (BC) with random fading and imperfect feedback, and analyzes the throughput performance as a function of feedback statistics and cache size. In this setting, our work identifies the optimal cache-aided degrees-of-freedom (DoF) within a factor of 4, by identifying near-optimal schemes that exploit the new synergy between coded caching and delayed CSIT, as well as by exploiting the unexplored interplay between caching and feedback-quality. The derived limits interestingly reveal that --- the combination of imperfect quality current CSIT, delayed CSIT, and coded caching, guarantees that --- the DoF gains have an initial offset defined by the quality of current CSIT, and then that the additional gains attributed to coded caching are exponential, in the sense that any linear decrease in the required DoF performance, allows for an exponential reduction in the required cache size.Comment: 14 pages, 2 figures, submission Trans IT, V

The Synergistic Gains of Coded Caching and Delayed Feedback

In this paper, we consider the $K$-user cache-aided wireless MISO broadcast channel (BC) with random fading and delayed CSIT, and identify the optimal cache-aided degrees-of-freedom (DoF) performance within a factor of 4. The achieved performance is due to a scheme that combines basic coded-caching with MAT-type schemes, and which efficiently exploits the prospective-hindsight similarities between these two methods. This delivers a powerful synergy between coded caching and delayed feedback, in the sense that the total synergistic DoF-gain can be much larger than the sum of the individual gains from delayed CSIT and from coded caching. The derived performance interestingly reveals --- for the first time --- substantial DoF gains from coded caching, even when the (normalized) cache size $\gamma$ (fraction of the library stored at each receiving device) is very small. Specifically, a microscopic $\gamma \approx e^{-G}$ can come within a factor of $G$ from the interference-free optimal. For example, storing at each device only a \emph{thousandth} of what is deemed as `popular' content ($\gamma\approx 10^{-3}$), we approach the interference-free optimal within a factor of $ln(10^3) \approx 7$ (per user DoF of $1/7$), for any number of users. This result carries an additional practical ramification as it reveals how to use coded caching to essentially buffer CSI, thus partially ameliorating the burden of having to acquire real-time CSIT.Comment: 7 pages. Smaller part from a bigger journal submission arXiv:1511.0396

Feedback-Aided Coded Caching for the MISO BC with Small Caches

This work explores coded caching in the symmetric $K$-user cache-aided MISO BC with imperfect CSIT-type feedback, for the specific case where the cache size is much smaller than the library size. Building on the recently explored synergy between caching and delayed-CSIT, and building on the tradeoff between caching and CSIT quality, the work proposes new schemes that boost the impact of small caches, focusing on the case where the cumulative cache size is smaller than the library size. For this small-cache setting, based on the proposed near-optimal schemes, the work identifies the optimal cache-aided degrees-of-freedom (DoF) performance within a factor of 4.Comment: 8 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1511.0396