Xuanxuan Lu

Optimal linear precoding and postcoding for MIMO multi-sensor noisy observation problem

This paper proposes an efficient method for optimal joint precoding-postcoding design in a multi-input multi-output (MIMO) multi-sensor noisy observation context - a problem that is of great interest to the multi-relay MIMO transmission system. A set of wireless sensors, each provisioned with a different number of antennas and a different power constraint, precode and send their noisy observations of the same data to a common fusion center, which postcodes the data to make a best estimate of the original data. Taking the mean square error as a performance metric, we show that the optimal joint precoding-postcoding design problem is non-convex. Leveraging the alternative minimization framework, we are able to decompose it to two convex subproblems, one of which promises closed-form solutions. However, unlike previous studies that assume a total power constraint, the condition of individual power constraint and individual noise uncertainty at each sensor has tremendously complicated the second convex subproblem. Rather than numerically solve it via conventional convex optimization tools, we attack it analytically by transforming, approximating, and decomposing it to a set of new problems. We show that the new problems can be efficiently tackled via the Karush-Kuhn-Tucker conditions in an iterative manner. Simultions show that it leads to a convergence much faster and more robust than the conventional convex optimization tools.

Achieving FEC and RLL for VLC: A Concatenated Convolutional-Miller Coding Mechanism

Run-length limited (RLL) codes are widely used in visible light communications to avoid long runs of 1s and 0s that potentially cause the flicker. This letter explores the serial concatenation of convolutional codes and Miller codes to simultaneously achieve forward error correction and RLL control. Miller codes with high bandwidth efficiency are much ignored in practice due to their disappointing power efficiency. The novelty of this letter is that we identity the merit of this previously unfavorable RLL code (i.e., trellis structure and soft decidability), exploit some important coding principles (i.e., interleaved serial concatenation and soft-iterative decoding), and assemble it to a powerful turbo structure that makes it outperform the existing favorable choices. A modified Bahl-Cocke-Jelinek-Raviv decoding algorithm is developed for the proposed concatenation. Analysis and simulations confirm that the new system is capable of solid RLL control and a superb performance better than the existing schemes.

Soft-encoding distributed coding for parallel relay systems

In the paper, a new distributed coding scheme for parallel relay systems is proposed, in which a sender communicates to a destination that is two hops away via two (or more) parallel relays. The key idea is the exploitation of a (rate-1) soft convolutional encoder at each of the parallel relays, to collaboratively form a simple but powerful distributed analog coding scheme to achieve efficient forwarding of soft reliability messages. We detail the encoding and decoding process of the proposed soft-encoding distributed coding. As the input of the encoder would affect the overall performance, we analyze what form of messages at the relay is most appropriate to be forwarded to the destination. The range-limited log likelihood ratio (range-limited LLR) is chosen as the input. The optimality of the range-limited LLRs as the best form of relaying messages is verified by the simulation results. Our new distributed coding scheme can obviously outperform the existing ones.

Multi-terminal joint transceiver design for MIMO systems with contaminated source and individual power constraint

This paper considers optimal transceiver design for a multi-terminal multi-inputmulti-output (MIMO) system, where L sensors wirelessly communicate individually-contaminated observations of the same source to the fusion center. The constraint that each sensor has individual power cap significantly complicates the non-convex optimization problem, and the optimal (linear) precoding and postcoding are not previously known. Using the signal-to-noise-ratio (SNR) as the performance metric, and employing the alternative minimization approach, we decompose the original problem into multiple subproblems that will run iteratively. The key results include the development of a closed-form solution to the optimal postcoder given the precoders, and the development of a closed-form solution for the ε-optimal precoders given the postcoder. The former is achieved via eigenvalue decomposition, and the latter is achieved by bounding the optimal solutions from above and from below, designing a series of fast-converging bisection search, and developing the closed-form analytical solution for each search. The convergence and the complexity of the proposed algorithm is analyzed and simulations are provided to confirm the efficiency of our proposal.

A novel SISO trellis strategy for relaying distorted signals in wireless networks

We consider the relaying of binary antipodal signals across two hops via soft regeneration and soft error protection. The signals at the input of the regenerator are degraded by additive white Gaussian noise (AWGN). Traditional approaches either directly relay the noisy analog waveform to the destination (thus missing the opportunity for coding gain), or make hard detection and then re-encode the bits using a digital error correction code (which may risk error propagation). This paper proposes a new class of soft-input soft-output (SISO) encoding strategies that are shown to outperform the conventional hard and soft forwarding schemes. Making essential use of the trellis structure, the soft encoder and the maximum likelihood decoder both operate efficiently in linear time, and support variable block sizes and code rates. Practical applications in relay communication are discussed. Simulations confirm the outstanding performance of the proposed scheme.

New Soft-Encoding Relay (SoER) Mechanisms for Wireless Relay Systems: Convolutional and Turbo Constructions

A two-hop parallel-relay network is considered in this paper. Conventional schemes investigating the coding strategies at the relay(s) have largely focused on hard encoding, with the exception of one pioneering strategy that proposed a soft distributed encoding using the soft estimate (tanh-based) information. To fully harness the gain promised by soft encoding, this paper focuses on distributed soft encoding strategies at the relays. Unlike the previous work that favors the tanh form for soft encoding, we advocate the range-limited log-likelihood ratios (rLLR) as a better way for the relays to capture the reliability of the messages sent by the sender, and especially to further soft-encode these messages. Based on this, we develop a simple but effective soft-encoding relay (SoER) strategy that exploits the useful features of rLLR. Specifically, the close resemblance of rLLR to the tanh form allows us to derive a very simple convolutional encoding, and the piece-wise linearity of rLLR allows us to evaluate the codeword probability density function (PDF) analytically, which further allows us to derive a Viterbi decoding algorithm using a more precise PDF (in addition to the Gaussian-approximated Viterbi algorithm). We finally extend the nonrecursive convolutional SoER strategy to the turbo SoER strategy. Simulation results confirm the efficiency of the new proposed SoER schemes.

A parametric approach to optimal soft signal relaying in wireless parallel-relay systems

This paper proposes an optimal estimate-forward strategy, termed Z-forwarding, for 2-hop parallel-relay systems. The previous tanh-forwarding strategy, which is optimized for the single-relay system is shown to be no longer optimal for a parallel-relay system. Instead, a new, parametrically-optimized Z-forwarding strategy is proposed, where the relay re-transmits a nonlinear but piece-wise linear function of the log-likelihood ratio (LLR) of the source signal. By analytically formulating the end-to-end bit error rate (BER), optimal thresholds that minimize the BER are computed as a function of all the source-relay and relay-destination channels. Maximum likelihood (ML) detector is also developed for the destination to recoup all the diversity gains from the multiple relays. It is shown that Z-forwarding strategy delivers a performance comparable to tanh-forwarding in a single relay system, but considerably better than tanh-forwarding (as well as amplify-forward and decode-forward) in a parallel-relay system.

A new forwarding strategy for wireless relay channels: Analog-encode-and-forward (AEF)

Amplify-forward (AF) and decode-forward (DF) continue to dominate the practical strategies for signal relaying. Amplify-forward is a way of forwarding soft reliability information that is extracted directly from the channel reception - without making use of the channel code that may well exist in the packet, whereas decode-forward exploits the coding gain, but forwards only the hard-decisions (provided that decoder succeeds). This paper joins the merits of AF and DF by exploiting “analog codes” - a special class of error correction codes that can directly encode and protect real-valued data. Exploiting useful ideas from the chaos theory and the parallel concatenation structure, we show that how chaos-based analog turbo-like codes can be designed and used in user cooperation. In the proposed “analog-encode-forward (AEF)” scheme, the relay node first soft-decodes the packet from the source, then re-encodes this soft decoder output using an appropriate analog code, and forwards it to the destination. A hybrid scheme that combines AEF and DF is further exploited to improve performance.

Joint Transceiver Design for Linear MMSE Data Fusion in Coherent MAC Wireless Sensor Networks

Abstract This paper considers the design of minimal mean square error (MMSE) transceivers in a wireless sensor network. The problem is nonconvex and challenging, and previous results (with partial solutions and/or with convergence unproved) left much to be desired. Here we propose several approaches – 2 block coordinate descent (BCD), essentially cyclic multi-block method and its variants and distributive method to solve this problem. The proposed 2-BCD approach formulates the subproblem of joint beamformer optimization as a general second-order cone programming problem, which lends itself to standard numerical solvers and which requires no extra assumptions like previous works do. The proposed essentially cyclic multi-block approach further decomposes the joint beamformer design subproblem into multiple blocks, and rigorously solves each with semi-closed-form solution. The distributive algorithm optimizes transmitters in a decentralized manner and has never been considered in existing literature. The distributive algorithm has time complexity independent of number of sensors and is especially suitable for large-scale networks. All the previous BCD-based approaches left some singularity issue unattended as well as the convergence property unaddressed, our proposals are the first to provide a complete and provably-converging analytical solution. Extensive analysis and simulations demonstrate the merits of the novel approaches relative to existing alternatives.

Cooperative Transmission Through Signal-Superposition-Based Braid Coding

This paper investigates a cooperative transmission scheme for a multisource single-destination system through superposition modulation based on braid coding. The source nodes take turns transmitting, and each time, a source “overlays” its new data together with (some or all of) what it overhears from its partner(s), in a way similar to French braiding the hair. We show that the proposed “braid coding” cooperative scheme benefits not only from the cooperative diversity but from the bit error rate (BER) performance gain as well. We introduce two subclasses of braid coding, namely, the nonregenerative and regenerative cases, and, using the pairwise error probability (PEP) as a figure of merit, derive the optimal weight parameters for each one. By exploiting the structure relevance of braid codes with trellis codes, we propose a Viterbi maximum-likelihood (ML) decoding method of linear complexity for the regenerative case; we also investigate and compare several linear detectors for the nonregenerative case. We analyze the theoretical BER performance of the proposed scheme and prove that the full diversity order can be achieved using braid coding. Moreover, we discuss the memory size that strikes the best balance between performance and complexity by considering both the (Euclidean) free distance and the diversity order. The proposed braid coding can be viewed as a special case of network coding. Finally, we present soft-iterative joint channel-network decoding. The overall decoding process is divided into forward message passing and backward message passing, which makes effective use of the available reliability information from all the received signals. Simulation results confirm the efficacy and efficiency of the proposed scheme.