83,275 research outputs found

    Distortion Exponent in MIMO Fading Channels with Time-Varying Source Side Information

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    Transmission of a Gaussian source over a time-varying multiple-input multiple-output (MIMO) channel is studied under strict delay constraints. Availability of a correlated side information at the receiver is assumed, whose quality, i.e., correlation with the source signal, also varies over time. A block-fading model is considered for the states of the time-varying channel and the time-varying side information; and perfect state information at the receiver is assumed, while the transmitter knows only the statistics. The high SNR performance, characterized by the \textit{distortion exponent}, is studied for this joint source-channel coding problem. An upper bound is derived and compared with lowers based on list decoding, hybrid digital-analog transmission, as well as multi-layer schemes which transmit successive refinements of the source, relying on progressive and superposed transmission with list decoding. The optimal distortion exponent is characterized for the single-input multiple-output (SIMO) and multiple-input single-output (MISO) scenarios by showing that the distortion exponent achieved by multi-layer superpositon encoding with joint decoding meets the proposed upper bound. In the MIMO scenario, the optimal distortion exponent is characterized in the low bandwidth ratio regime, and it is shown that the multi-layer superposition encoding performs very close to the upper bound in the high bandwidth expansion regime.Comment: Submitted to IEEE Transactions on Information Theor

    Optimal rate list decoding via derivative codes

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    The classical family of [n,k]q[n,k]_q Reed-Solomon codes over a field \F_q consist of the evaluations of polynomials f \in \F_q[X] of degree <k< k at nn distinct field elements. In this work, we consider a closely related family of codes, called (order mm) {\em derivative codes} and defined over fields of large characteristic, which consist of the evaluations of ff as well as its first m−1m-1 formal derivatives at nn distinct field elements. For large enough mm, we show that these codes can be list-decoded in polynomial time from an error fraction approaching 1−R1-R, where R=k/(nm)R=k/(nm) is the rate of the code. This gives an alternate construction to folded Reed-Solomon codes for achieving the optimal trade-off between rate and list error-correction radius. Our decoding algorithm is linear-algebraic, and involves solving a linear system to interpolate a multivariate polynomial, and then solving another structured linear system to retrieve the list of candidate polynomials ff. The algorithm for derivative codes offers some advantages compared to a similar one for folded Reed-Solomon codes in terms of efficient unique decoding in the presence of side information.Comment: 11 page

    Slepian-Wolf Coding for Broadcasting with Cooperative Base-Stations

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    We propose a base-station (BS) cooperation model for broadcasting a discrete memoryless source in a cellular or heterogeneous network. The model allows the receivers to use helper BSs to improve network performance, and it permits the receivers to have prior side information about the source. We establish the model's information-theoretic limits in two operational modes: In Mode 1, the helper BSs are given information about the channel codeword transmitted by the main BS, and in Mode 2 they are provided correlated side information about the source. Optimal codes for Mode 1 use \emph{hash-and-forward coding} at the helper BSs; while, in Mode 2, optimal codes use source codes from Wyner's \emph{helper source-coding problem} at the helper BSs. We prove the optimality of both approaches by way of a new list-decoding generalisation of [8, Thm. 6], and, in doing so, show an operational duality between Modes 1 and 2.Comment: 16 pages, 1 figur
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