arXiv subjects

Petros Elia

Publications and source records attributed to Petros Elia.

68 records · Page 4Linked to original sources

arXiv2012

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.

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arXiv2012

Degrees-of-Freedom Region of the MISO Broadcast Channel with General Mixed-CSIT

In the setting of the two-user broadcast channel, recent work by Maddah-Ali and Tse has shown that knowledge of prior channel state information at the transmitter (CSIT) can be useful, even in the absence of any knowledge of current CSIT. Very recent work by Kobayashi et al., Yang et al., and Gou and Jafar, extended this to the case where, instead of no current CSIT knowledge, the transmitter has partial knowledge, and where under a symmetry assumption, the quality of this knowledge is identical for the different users' channels. Motivated by the fact that in multiuser settings, the quality of CSIT feedback may vary across different links, we here generalize the above results to the natural setting where the current CSIT quality varies for different users' channels. For this setting we derive the optimal degrees-of-freedom (DoF) region, and provide novel multi-phase broadcast schemes that achieve this optimal region. Finally this generalization incorporates and generalizes the corresponding result in Maleki et al. which considered the broadcast channel with one user having perfect CSIT and the other only having prior CSIT.

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arXiv2011

Achieving a vanishing SNR-gap to exact lattice decoding at a subexponential complexity

The work identifies the first lattice decoding solution that achieves, in the general outage-limited MIMO setting and in the high-rate and high-SNR limit, both a vanishing gap to the error-performance of the (DMT optimal) exact solution of preprocessed lattice decoding, as well as a computational complexity that is subexponential in the number of codeword bits. The proposed solution employs lattice reduction (LR)-aided regularized (lattice) sphere decoding and proper timeout policies. These performance and complexity guarantees hold for most MIMO scenarios, all reasonable fading statistics, all channel dimensions and all full-rate lattice codes. In sharp contrast to the above manageable complexity, the complexity of other standard preprocessed lattice decoding solutions is shown here to be extremely high. Specifically the work is first to quantify the complexity of these lattice (sphere) decoding solutions and to prove the surprising result that the complexity required to achieve a certain rate-reliability performance, is exponential in the lattice dimensionality and in the number of codeword bits, and it in fact matches, in common scenarios, the complexity of ML-based solutions. Through this sharp contrast, the work was able to, for the first time, rigorously quantify the pivotal role of lattice reduction as a special complexity reducing ingredient. Finally the work analytically refines transceiver DMT analysis which generally fails to address potentially massive gaps between theory and practice. Instead the adopted vanishing gap condition guarantees that the decoder's error curve is arbitrarily close, given a sufficiently high SNR, to the optimal error curve of exact solutions, which is a much stronger condition than DMT optimality which only guarantees an error gap that is subpolynomial in SNR, and can thus be unbounded and generally unacceptable in practical settings.

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arXiv2011

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.

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arXiv2010

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.

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arXiv2009

Large Families of Optimal Two-Dimensional Optical Orthogonal Codes

Nine new 2-D OOCs are presented here, all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature. Each of these constructions is either optimal or asymptotically optimal with respect to either the original Johnson bound or else a non-binary version of the Johnson bound introduced in this paper. The first 5 codes are constructed using polynomials over finite fields - the first construction is optimal while the remaining 4 are asymptotically optimal. The next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal. The last two codes, also asymptotically optimal, are constructed by composing two of the above codes with a constant weight binary code. Also presented, is a three-dimensional OOC that exploits the polarization dimension. Finally, phase-encoded optical CDMA is considered and construction of two efficient codes are provided.

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arXiv2009

DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models

The work identifies the first general, explicit, and non-random MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive maximum-likelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their lattice-reduction (LR)-aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular lattice-code applied. As a special case, it is established that the LLL-based LR-aided linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worst-case complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in rate. The results' generality lends them applicable to a plethora of pertinent communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI, cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality of the LR-aided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.

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arXiv2009

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.

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arXiv2008

High-SNR Analysis of Outage-Limited Communications with Bursty and Delay-Limited Information

This work analyzes the high-SNR asymptotic error performance of outage-limited communications with fading, where the number of bits that arrive at the transmitter during any time slot is random but the delivery of bits at the receiver must adhere to a strict delay limitation. Specifically, bit errors are caused by erroneous decoding at the receiver or violation of the strict delay constraint. Under certain scaling of the statistics of the bit-arrival process with SNR, this paper shows that the optimal decay behavior of the asymptotic total probability of bit error depends on how fast the burstiness of the source scales down with SNR. If the source burstiness scales down too slowly, the total probability of error is asymptotically dominated by delay-violation events. On the other hand, if the source burstiness scales down too quickly, the total probability of error is asymptotically dominated by channel-error events. However, at the proper scaling, where the burstiness scales linearly with 1/sqrt(log SNR) and at the optimal coding duration and transmission rate, the occurrences of channel errors and delay-violation errors are asymptotically balanced. In this latter case, the optimal exponent of the total probability of error reveals a tradeoff that addresses the question of how much of the allowable time and rate should be used for gaining reliability over the channel and how much for accommodating the burstiness with delay constraints.

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arXiv2007

Approximately-Universal Space-Time Codes for the Parallel, Multi-Block and Cooperative-Dynamic-Decode-and-Forward Channels

Explicit codes are constructed that achieve the diversity-multiplexing gain tradeoff of the cooperative-relay channel under the dynamic decode-and-forward protocol for any network size and for all numbers of transmit and receive antennas at the relays. A particularly simple code construction that makes use of the Alamouti code as a basic building block is provided for the single relay case. Along the way, we prove that space-time codes previously constructed in the literature for the block-fading and parallel channels are approximately universal, i.e., they achieve the DMT for any fading distribution. It is shown how approximate universality of these codes leads to the first DMT-optimum code construction for the general, MIMO-OFDM channel.

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arXiv2006

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

We consider cooperative relay communication in a fading channel environment under the Orthogonal Amplify and Forward (OAF) and Orthogonal and Non-Orthogonal Selection Decode and Forward (OSDF and NSDF) protocols. For all these protocols, we compute the Diversity-Multiplexing Gain Tradeoff (DMT). We construct DMT optimal codes for the protocols which are sphere decodable and, in certain cases, incur minimum possible delay. Our results establish that the DMT of the OAF protocol is identical to the DMT of the Non-Orthogonal Amplify and Forward (NAF) protocol. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time duration for which the source alone transmits is allowed to vary with the rate of communication. Among the class of static amplify-and-forward and decode-and-forward protocols, the variable-NSDF protocol is shown to have the best known DMT for any number of relays apart from the two-relay case. When there are two relays, the variable-NSDF protocol is shown to improve on the DMT of the best previously-known protocol for higher values of the multiplexing gain. Our results also establish that the fixed-NSDF protocol has a better DMT than the NAF protocol for any number of relays. Finally, we present a DMT optimal code construction for the NAF protocol.

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arXiv2006

Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff

A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) block code. This tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>= n_t+n_r-1 where T is the number of time slots over which coding takes place and n_t,n_r are the number of transmit and receive antennas respectively. For T < n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available. In this paper, we present a complete solution to the problem of explicitly constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff for any number of receive antennas. We do this by showing that for the square minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes having the non-vanishing determinant property are D-MG optimal. While constructions of such codes were previously known for restricted values of n, we provide here a construction for such codes that is valid for all n. For the rectangular, T > n_t case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is the same as that previously known to hold for T >= n_t + n_r -1.

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arXiv2005

Approximately universal optimality over several dynamic and non-dynamic cooperative diversity schemes for wireless networks

In this work we explicitly provide the first ever optimal, with respect to the Zheng-Tse diversity multiplexing gain (D-MG) tradeoff, cooperative diversity schemes for wireless relay networks. The schemes are based on variants of perfect space-time codes and are optimal for any number of users and all statistically symmetric (and in some cases, asymmetric) fading distributions. We deduce that, with respect to the D-MG tradeoff, channel knowledge at the intermediate relays and infinite delay are unnecessary. We also show that the non-dynamic selection decode and forward strategy, the non-dynamic amplify and forward, the non-dynamic receive and forward, the dynamic amplify and forward and the dynamic receive and forward cooperative diversity strategies allow for exactly the same D-MG optimal performance.

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arXiv2005

Perfect Space-Time Codes with Minimum and Non-Minimum Delay for Any Number of Antennas

Perfect space-time codes were first introduced by Oggier et. al. to be the space-time codes that have full rate, full diversity-gain, non-vanishing determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping of the constellation. These defining conditions jointly correspond to optimality with respect to the Zheng-Tse D-MG tradeoff, independent of channel statistics, as well as to near optimality in maximizing mutual information. All the above traits endow the code with error performance that is currently unmatched. Yet perfect space-time codes have been constructed only for 2,3,4 and 6 transmit antennas. We construct minimum and non-minimum delay perfect codes for all channel dimensions.

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