Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor

Paraunitary oversampled filter bank design for channel coding

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a design for the decoder's synthesis filter bank in order to minimise the noise power in the decoded signal, subject to admitting perfect reconstruction through paraunitarity of the filter bank. We demonstrate that this approach can lead to a significant reduction of the noise interference by exploiting both the correlation of the channel and the redundancy of the filter banks. Simulation results providing some insight into these mechanisms are provided

Wi-Fi Teeter-Totter: Overclocking OFDM for Internet of Things

The conventional high-speed Wi-Fi has recently become a contender for low-power Internet-of-Things (IoT) communications. OFDM continues its adoption in the new IoT Wi-Fi standard due to its spectrum efficiency that can support the demand of massive IoT connectivity. While the IoT Wi-Fi standard offers many new features to improve power and spectrum efficiency, the basic physical layer (PHY) structure of transceiver design still conforms to its conventional design rationale where access points (AP) and clients employ the same OFDM PHY. In this paper, we argue that current Wi-Fi PHY design does not take full advantage of the inherent asymmetry between AP and IoT. To fill the gap, we propose an asymmetric design where IoT devices transmit uplink packets using the lowest power while pushing all the decoding burdens to the AP side. Such a design utilizes the sufficient power and computational resources at AP to trade for the transmission (TX) power of IoT devices. The core technique enabling this asymmetric design is that the AP takes full power of its high clock rate to boost the decoding ability. We provide an implementation of our design and show that it can reduce the IoT's TX power by boosting the decoding capability at the receivers

Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals

We consider the efficient quantization of a class of nonbandlimited signals, namely, the class of discrete-time signals that can be recovered from their decimated version. The signals are modeled as the output of a single FIR interpolation filter (single band model) or, more generally, as the sum of the outputs of L FIR interpolation filters (multiband model). These nonbandlimited signals are oversampled, and it is therefore reasonable to expect that we can reap the same benefits of well-known efficient A/D techniques that apply only to bandlimited signals. We first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals. We can achieve a substantial decrease in bit rate by appropriately decimating the signals and then quantizing them. To further increase the effective quantizer resolution, noise shaping is introduced by optimizing prefilters and postfilters around the quantizer. We start with a scalar time-invariant quantizer and study two important cases of linear time invariant (LTI) filters, namely, the case where the postfilter is the inverse of the prefilter and the more general case where the postfilter is independent from the prefilter. Closed form expressions for the optimum filters and average minimum mean square error are derived in each case for both the single band and multiband models. The class of noise shaping filters and quantizers is then enlarged to include linear periodically time varying (LPTV)M filters and periodically time-varying quantizers of period M. We study two special cases in great detail

Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to $1-{Q}/{N}$. Here, $N$ is the number of symbols transmitted within one fading block, and $Q$ is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as $1-1/N$. Since the capacity pre-log corresponding to symbol-rate sampling is $1-Q/N$, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.Comment: To appear in the IEEE Transactions on Information Theor

Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems

We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with oversampling factors of at least two, we provide prescriptions for the shortest filter length of the synthesis bank that would guarantee PR almost surely. The prescribed length is as short or shorter than the analysis filters and has an approximate inverse relationship with the oversampling factor. Our results are in form of necessary and sufficient statements that hold generically, hence only fail for elaborately-designed nongeneric examples. We provide extensive numerical verification of the theoretical results and demonstrate that the gap between the derived filter length prescriptions and the true minimum is small. The results have potential applications in synthesis FB design problems, where the analysis bank is given, and for analysis of fundamental limitations in blind signals reconstruction from data collected by unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin