On the Combinatorial Version of the Slepian-Wolf Problem

We study the following combinatorial version of the Slepian-Wolf coding scheme. Two isolated Senders are given binary strings $X$ and $Y$ respectively; the length of each string is equal to $n$, and the Hamming distance between the strings is at most $\alpha n$. The Senders compress their strings and communicate the results to the Receiver. Then the Receiver must reconstruct both strings $X$ and $Y$. The aim is to minimise the lengths of the transmitted messages. For an asymmetric variant of this problem (where one of the Senders transmits the input string to the Receiver without compression) with deterministic encoding a nontrivial lower bound was found by A.Orlitsky and K.Viswanathany. In our paper we prove a new lower bound for the schemes with syndrome coding, where at least one of the Senders uses linear encoding of the input string. For the combinatorial Slepian-Wolf problem with randomized encoding the theoretical optimum of communication complexity was recently found by the first author, though effective protocols with optimal lengths of messages remained unknown. We close this gap and present a polynomial time randomized protocol that achieves the optimal communication complexity.Comment: 20 pages, 14 figures. Accepted to IEEE Transactions on Information Theory (June 2018

Frame Permutation Quantization

Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of possible quantization rates and a higher maximum rate. Various representations for the partitions induced by FPQ are presented, and reconstruction algorithms based on linear programming, quadratic programming, and recursive orthogonal projection are derived. Implementations of the linear and quadratic programming algorithms for uniform and Gaussian sources show performance improvements over entropy-constrained scalar quantization for certain combinations of vector dimension and coding rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared error (MSE) decays as 1/M^4 for an M-element frame, which is consistent with previous results on optimal decay of MSE. Reconstruction using the canonical dual frame is also studied, and several results relate properties of the analysis frame to whether linear reconstruction techniques provide consistent reconstructions.Comment: 29 pages, 5 figures; detailed added to proof of Theorem 4.3 and a few minor correction

Application of Expurgated PPM to Indoor Visible Light Communications - Part I: Single-User Systems

Visible light communications (VLC) in indoor environments suffer from the limited bandwidth of LEDs as well as from the inter-symbol interference (ISI) imposed by multipath. In this work, transmission schemes to improve the performance of indoor optical wireless communication (OWC) systems are introduced. Expurgated pulse-position modulation (EPPM) is proposed for this application since it can provide a wide range of peak to average power ratios (PAPR) needed for dimming of the indoor illumination. A correlation decoder used at the receiver is shown to be optimal for indoor VLC systems, which are shot noise and background-light limited. Interleaving applied on EPPM in order to decrease the ISI effect in dispersive VLC channels can significantly decrease the error probability. The proposed interleaving technique makes EPPM a better modulation option compared to PPM for VLC systems or any other dispersive OWC system. An overlapped EPPM pulse technique is proposed to increase the transmission rate when bandwidth-limited white LEDs are used as sources.Comment: Journal of Lightwave Technolog

On achievable rates for multicast in the presence of side information

We investigate the network source coding rate region for networks with multiple sources and multicast demands in the presence of side information, generalizing earlier results on multicast rate regions without side information. When side information is present only at the terminal nodes, we show that the rate region is precisely characterized by the cut-set bounds and that random linear coding suffices to achieve the optimal performance. When side information is present at a non-terminal node, we present an achievable region. Finally, we apply these results to obtain an inner bound on the rate region for networks with general source-demand structures