Avi Steiner

A broadcast approach for a single-user slowly fading MIMO channel

A broadcast transmission strategy for the slowly fading Gaussian multiple-input multiple-output (MIMO) channel is introduced. This broadcast strategy is an extension of the single-input single-output (SISO) broadcast approach. Perfect channel state information (CSI) is assumed known at the receiver end only. This strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter. Transmission of layered coded information is motivated by the theory of majorization. We derive the basic equations characterizing achievable rates of the strategy. Several ad hoc approximations to the achievable region are considered and their performance is compared with the SISO setting and the ergodic capacity. It has been demonstrated that a single-layer outage approach is reasonably efficient in the MIMO setting in terms of the average reliably decoded rate. A multiple-access channel (MAC) broadcast approach is also applied for the MIMO case, and demonstrated to be relatively efficient.

Successive Refinement Via Broadcast: Optimizing Expected Distortion of a Gaussian Source Over a Gaussian Fading Channel

We consider the problem of transmitting a Gaussian source on a slowly fading Gaussian channel, subject to the mean-squared error distortion measure. The channel state information is known only at the receiver but not at the transmitter. The source is assumed to be encoded in a successive refinement (SR) manner, and then transmitted over the channel using the broadcast strategy. In order to minimize the expected distortion at the receiver, optimal power allocation is essential. We propose an efficient algorithm to compute the optimal solution in linear time , when the total number of possible discrete fading states. Moreover, we provide a derivation of the optimal power allocation when the fading state is a continuum, using the classical variational method. The proposed algorithm as well as the continuous solution is based on an alternative representation of the capacity region of the Gaussian broadcast channel.

Single-User Broadcasting Protocols Over a Two-Hop Relay Fading Channel

A two-hop relay fading channel is considered, where only decoders possess perfect channel state information (CSI). Various relaying protocols and broadcasting strategies are studied. The main focus of this work is on simple relay transmission scheduling schemes. For decode-and-forward (DF) relaying, the simple relay cannot buffer multiple packets, nor can it reschedule retransmissions. This gives rise to consideration of other relaying techniques, such as amplify-and-forward (AF), where a maximal broadcasting achievable rate is analytically derived. A quantize-and-forward (QF) relay, coupled with a single-level code at the source, uses codebooks matched to the received signal power and performs optimal quantization. This is simplified by a hybrid amplify-QF (AQF) relay, which performs scaling, and single codebook quantization on the input. It is shown that the latter is optimal by means of throughput on the relay-destination link, while maintaining a lower coding complexity than the QF setting. A further extension of the AQF allows the relay to perform successive refinement, coupled with a matched multilevel code. Numerical results show that for high signal-to-noise ratios (SNRs), the broadcast approach over AF relay may achieve higher throughput gains than other relaying protocols that are numerically tractable

Broadcast Cooperation Strategies for Two Colocated Users

This work considers the problem of communication between a remote single transmitter and a destined user, with helping colocated users, over an independent block Rayleigh-fading channel. The colocation nature of the users allows cooperation, which increases the overall achievable rate, from transmitter to destination. The transmitter is ignorant of the fading coefficients, while receivers have access to perfect channel state information (CSI). We propose, for this setting, a multilayer broadcast transmission approach. The broadcast approach enables enhanced cooperation between the colocated users. That is due to the nature of broadcasting, where the better the channel quality, the more layers that can reliably be decoded. The cooperation between the users is performed over additive white Gaussian noise (AWGN) channels, with a relaying power constraint, and unlimited bandwidth. Three commonly used cooperation techniques are studied: amplify-and-forward (AF), compress-and-forward (CF), and decode-and-forward (DF). These techniques are extended by using the broadcast approach for the case of relaxed decoding delay constraint. For this case, a separate processing of the layers, which includes multisession cooperation is shown to be beneficial. Further, closed-form expressions for infinitely many AF sessions and recursive expressions for the more complex CF are given. Numerical results for the various cooperation strategies demonstrate how the multisession cooperation outperforms conventional relaying techniques.

Multi-layer broadcasting hybrid-ARQ strategies for block fading channels

Conventional hybrid automatic retransmission request (HARQ) is usually used to maximize throughput. However, high throughput is achieved at the expense of high latency. We study a novel broadcasting HARQ strategy. The multi-layer broadcast approach is suitable for the case where transmitter has no channel state information (CSI), which is the case with HARQ schemes as well. The broadcast approach enables the receiver to decode rates, which are matched to every fading gain realization. That is, the higher the fading gain realization, the more layers are reliably decoded. The broadcast approach combined with HARQ enables achieving high throughput with low latency. In a broadcast HARQ scheme every code layer supports HARQ independently. Thus HARQ is applied in every transmission block to undecoded layers only, which highly increases the broadcast approach efficiency. In this paper, both broadcast chase combining (BCC) HARQ and broadcast incremental redundancy (BIR) HARQ are studied in the limit of infinitely many layers, and for finite level coding. Interestingly, with continuous broadcasting the BCC-HARQ is found to closely approximate the BIR-HARQ, while using a sub-optimal broadcasting power distribution.

Multi-Layer Broadcasting over a Block Fading MIMO Channel

This paper introduces extensions for the broadcast approach for a multi-input multi-output (MIMO) block fading channel, with receiver only channel state information (CSI). Previous works have not been able to fully characterize the fundamental MIMO broadcasting upper bound. As it seems that analytical solution for this problem is quite difficult to achieve, we consider here sub-optimal schemes, for which achievable rates may be computed. In particular, finite level coding over a MIMO channel instead of continuous layering is analyzed, the expressions derived for the decoding probability regions allow numerical computation of finite level coding upper bounds. Noticing that the gains of two level coding over a MIMO channel are rather small, we consider sub-optimal techniques, which are more straightforward to implement. Among these techniques is the multiple-access channel (MAC) approach with single level coded streams, which is similar in concept to V-BLAST. Closed form expressions for probabilities of decoding regions here are derived, allowing numerical evaluation. We further consider multi-access permutation codes (MAPC). A Hadamard transform is compared with a suggested diagonal permutation code, which are shown to have similar performance, while diagonal permutation has lower implementation complexity. For all approaches, we derive information theoretic upper bounds of achievable rates.

Achievable Rates with Imperfect Transmitter Side Information Using a Broadcast Transmission Strategy

rdquoWe investigate the performance of the broadcast approach for various fading distributions, which correspond to different models of partial transmit channel state information (CSI). The first model considered is the quantized limited feedback. In this model, the receiver can send as feedback only a finite number of bits describing the fading gain. We derive the optimal power allocation for the broadcast approach for the quantized feedback model. For a Rayleigh fading channel, numerical results here show that if the feedback word can be longer than one bit, the broadcasting gain becomes negligible, due to diminished channel uncertainty. The second partial transmit CSI model is a stochastic Gaussian model with mean and variance information, which is commonly used for modeling the channel estimation error. In a single-input single-output (SISO) channel, this model also corresponds to the Ricean fading distribution, for which we derive maximal achievable broadcasting rates. We further consider a multiple-input single-output (MISO) channel, and derive the optimal power allocation strategy in a broadcast approach. Numerical results here show that uniform power allocation is preferable over beamforming power allocation in the region where broadcasting gain over single level coding is non-negligible.

Iterative decoding of space-time differentially coded unitary matrix modulation

Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas is investigated. Codes achieving bit error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 0.8 to 2.8 dB from the capacity limit were found with coding rates of 0.5 to 2.25 bits per channel use. The codes are serial concatenation of a turbo code and a unitary matrix differential modulation code. The receiver is based on a high-performance joint iterative decoding of the turbo code and the modulation code. Information-theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.

On Queueing and Multilayer Coding

A single-server queue concatenated with a multilayer channel encoder is considered. The main focus of this work is on minimization of the expected delay of a packet from entering the queue until completion of successful service. Tight bounds are derived for the expected delay for different numbers of coded layers. Numerical optimization is applied to find the optimal resource allocation minimizing the average delay. Similar bounds are also derived for the case of continuous layering. It is demonstrated that code layering may give pronounced performance gains in terms of delay, which are more impressive than those associated with throughput. This makes layering more attractive when communicating under stringent delay constraints.

Turbo coded space-time unitary matrix differential modulation

Non-coherent communication over the Rayleigh flat fading channel with multiple transmit and receive antenna is investigated. Codes achieving a bit error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 0.8 to 2.8 dB from the channel capacity limit were found with coding rates of 0.5 to 2.25 bits per channel use. The codes are a serial concatenation of turbo code and a unitary matrix differential modulation code. The receiver is based on a high performance joint iterative decoding of the turbo code and the modulation code. Information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.