Capacity of a Class of State-Dependent Orthogonal Relay Channels

The class of orthogonal relay channels in which the orthogonal channels connecting the source terminal to the relay and the destination, and the relay to the destination, depend on a state sequence, is considered. It is assumed that the state sequence is fully known at the destination while it is not known at the source or the relay. The capacity of this class of relay channels is characterized, and shown to be achieved by the partial decode-compress-and-forward (pDCF) scheme. Then the capacity of certain binary and Gaussian state-dependent orthogonal relay channels are studied in detail, and it is shown that the compress-and-forward (CF) and partial-decode-and-forward (pDF) schemes are suboptimal in general. To the best of our knowledge, this is the first single relay channel model for which the capacity is achieved by pDCF, while pDF and CF schemes are both suboptimal. Furthermore, it is shown that the capacity of the considered class of state-dependent orthogonal relay channels is in general below the cut-set bound. The conditions under which pDF or CF suffices to meet the cut-set bound, and hence, achieve the capacity, are also derived.Comment: This paper has been accepted by IEEE Transactions on Information Theor

Joint Source-Channel Coding with Time-Varying Channel and Side-Information

Transmission of a Gaussian source over a time-varying Gaussian channel is studied in the presence of time-varying correlated side information at the receiver. A block fading model is considered for both the channel and the side information, whose states are assumed to be known only at the receiver. The optimality of separate source and channel coding in terms of average end-to-end distortion is shown when the channel is static while the side information state follows a discrete or a continuous and quasiconcave distribution. When both the channel and side information states are time-varying, separate source and channel coding is suboptimal in general. A partially informed encoder lower bound is studied by providing the channel state information to the encoder. Several achievable transmission schemes are proposed based on uncoded transmission, separate source and channel coding, joint decoding as well as hybrid digital-analog transmission. Uncoded transmission is shown to be optimal for a class of continuous and quasiconcave side information state distributions, while the channel gain may have an arbitrary distribution. To the best of our knowledge, this is the first example in which the uncoded transmission achieves the optimal performance thanks to the time-varying nature of the states, while it is suboptimal in the static version of the same problem. Then, the optimal \emph{distortion exponent}, that quantifies the exponential decay rate of the expected distortion in the high SNR regime, is characterized for Nakagami distributed channel and side information states, and it is shown to be achieved by hybrid digital-analog and joint decoding schemes in certain cases, illustrating the suboptimality of pure digital or analog transmission in general.Comment: Submitted to IEEE Transactions on Information Theor

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

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

Expected Distortion with Fading MIMO Channel and Side Information Quality

Projecte final de carrera fet en col.laboració amb CTTCCatalà: Considerem el problema de codificació conjunta de font i canal d'enviar una font Gaussiana sobre un canal fading multi-antena (MIMO) quan el decodificador té informació adicional correlada amb la font, amb una qualitat també variant amb el temps. Assumim un model block fading per ambdues qualitats del canal i la informació adicional, i assumim coneixement perfecte de canal a recepció, mentre que el transmissor només disposa de coneixement estadístic. Estem interessats en la distorsió quadràtica mitja d'aquest sistema. Estudiem separació en la codificació canal font, transmissió no codificada i dues tècniques de codificació conjunta de font i canal basades en decodificació conjunta a recepció: NBJD, que no utilitza binning no explicit i decodificació conjunta a recepció i HDA, que comprimeix la font i transmet l?error. Al decodificador, la paraula comprimida es recupera per decodificació conjunta amb l?error transmès i la informació adicional. Extenem aquestes tècniques a esquemes híbrids analògics-digitals i esquemes multi-capa. Estudiem numèricament el problema i donem resultats per el règim de SNR finita. Proporcionem expresions tancades per el Distortion exponent a regim de alta SNR. ////// Castellà: Consideramos el problema de codificación conjunta de fuente y canal de enviar una fuente Gaussiana sobre un canal fading multi-antena (MIMO) cuando el decodificador tiene información adicional correlada con la fuente, con una cualidad también variante en el tiempo. Asumimos un modelo block fading para ambas calidades del canal y la información adicional. Asumimos conocimiento perfecto de canal en recepción, mientras que el transmisor solo dispone de conocimiento estadístico. Estamos interesados en la distorsión cuadrática media de este sistema. Estudiamos separación en la codificación canal fuente, transmisión no codificada y dos técnicas de codificación conjunta de fuente y canal basadas en decodificación conjunta en recepción: NBJD, que no utiliza binning no explicito y decodificación conjunta, y HDA, que comprime la fuente y transmite el error. Al decodificar, la palabra comprimida es recuperada por decodificación conjunta entre el error transmitido y la información adicional. Extendemos estas técnicas a esquemas híbridos analógico-digitales y esquemas multi-capa. Estudiamos numéricamente el problema y damos resultados para el régimen de SNR finita. Proporcionamos expresiones cerradas para el Distortion exponent en régimen de alta SNR ////// English: We consider the joint source-channel coding problem of sending a Gaussian source over a multiple input-multiple output (MIMO) fading channel when the decoder has additional correlated side information whose quality is also time-varying. We assume a block fading model for both the channel and side information qualities, and assume perfect state information at the receiver, while the transmitter has only a statistical knowledge. We are interested in the expected squared-error distortion for this system. We study separate source-channel coding, uncoded transmission and two joint source-channel transmission schemes based on joint decoding at the receiver: NBJD, that uses no explicit binning and joint decoding of the side information and the channel output at the decoder and HDA, that compresses the source and transmits the error. At the decoder, the quantized codeword is recovered by means of joint decoding of the error and the side information. We extend such techniques to hybrid digital-analog and multi-layer schemes. We study numerically the problem and give results in the finite SNR regime. We provide closed form expressions for the distortion exponent in the high SNR regime

Lossy Compression for Compute-and-Forward in Limited Backhaul Uplink Multicell Processing

We study the transmission over a cloud radio access network in which multiple base stations (BS) are connected to a central processor (CP) via finite-capacity backhaul links. We propose two lattice-based coding schemes. In the first scheme, the base stations decode linear combinations of the transmitted messages, in the spirit of compute-and-forward (CoF), but differs from it essentially in that the decoded equations are remapped to linear combinations of the channel input symbols, sent compressed in a lossy manner to the central processor, and are not required to be linearly independent. Also, by opposition to the standard CoF, an appropriate multi-user decoder is utilized to recover the sent messages. The second coding scheme generalizes the first one by also allowing, at each relay node, a joint compression of the decoded equation and the received signal. Both schemes apply in general, but are more suited for situations in which there are more users than base stations. We show that both schemes can outperform standard CoF and successive Wyner-Ziv schemes in certain regimes, and illustrate the gains through some numerical examples.Comment: Submitted to IEEE Transactions on Communication

Expected Distortion with Fading MIMO Channel and Side Information Quality

Projecte final de carrera fet en col.laboració amb CTTCCatalà: Considerem el problema de codificació conjunta de font i canal d'enviar una font Gaussiana sobre un canal fading multi-antena (MIMO) quan el decodificador té informació adicional correlada amb la font, amb una qualitat també variant amb el temps. Assumim un model block fading per ambdues qualitats del canal i la informació adicional, i assumim coneixement perfecte de canal a recepció, mentre que el transmissor només disposa de coneixement estadístic. Estem interessats en la distorsió quadràtica mitja d'aquest sistema. Estudiem separació en la codificació canal font, transmissió no codificada i dues tècniques de codificació conjunta de font i canal basades en decodificació conjunta a recepció: NBJD, que no utilitza binning no explicit i decodificació conjunta a recepció i HDA, que comprimeix la font i transmet l?error. Al decodificador, la paraula comprimida es recupera per decodificació conjunta amb l?error transmès i la informació adicional. Extenem aquestes tècniques a esquemes híbrids analògics-digitals i esquemes multi-capa. Estudiem numèricament el problema i donem resultats per el règim de SNR finita. Proporcionem expresions tancades per el Distortion exponent a regim de alta SNR. ////// Castellà: Consideramos el problema de codificación conjunta de fuente y canal de enviar una fuente Gaussiana sobre un canal fading multi-antena (MIMO) cuando el decodificador tiene información adicional correlada con la fuente, con una cualidad también variante en el tiempo. Asumimos un modelo block fading para ambas calidades del canal y la información adicional. Asumimos conocimiento perfecto de canal en recepción, mientras que el transmisor solo dispone de conocimiento estadístico. Estamos interesados en la distorsión cuadrática media de este sistema. Estudiamos separación en la codificación canal fuente, transmisión no codificada y dos técnicas de codificación conjunta de fuente y canal basadas en decodificación conjunta en recepción: NBJD, que no utiliza binning no explicito y decodificación conjunta, y HDA, que comprime la fuente y transmite el error. Al decodificar, la palabra comprimida es recuperada por decodificación conjunta entre el error transmitido y la información adicional. Extendemos estas técnicas a esquemas híbridos analógico-digitales y esquemas multi-capa. Estudiamos numéricamente el problema y damos resultados para el régimen de SNR finita. Proporcionamos expresiones cerradas para el Distortion exponent en régimen de alta SNR ////// English: We consider the joint source-channel coding problem of sending a Gaussian source over a multiple input-multiple output (MIMO) fading channel when the decoder has additional correlated side information whose quality is also time-varying. We assume a block fading model for both the channel and side information qualities, and assume perfect state information at the receiver, while the transmitter has only a statistical knowledge. We are interested in the expected squared-error distortion for this system. We study separate source-channel coding, uncoded transmission and two joint source-channel transmission schemes based on joint decoding at the receiver: NBJD, that uses no explicit binning and joint decoding of the side information and the channel output at the decoder and HDA, that compresses the source and transmits the error. At the decoder, the quantized codeword is recovered by means of joint decoding of the error and the side information. We extend such techniques to hybrid digital-analog and multi-layer schemes. We study numerically the problem and give results in the finite SNR regime. We provide closed form expressions for the distortion exponent in the high SNR regime

Expected Distortion with Fading MIMO Channel and Side Information Quality

Projecte final de carrera fet en col.laboració amb CTTCCatalà: Considerem el problema de codificació conjunta de font i canal d'enviar una font Gaussiana sobre un canal fading multi-antena (MIMO) quan el decodificador té informació adicional correlada amb la font, amb una qualitat també variant amb el temps. Assumim un model block fading per ambdues qualitats del canal i la informació adicional, i assumim coneixement perfecte de canal a recepció, mentre que el transmissor només disposa de coneixement estadístic. Estem interessats en la distorsió quadràtica mitja d'aquest sistema. Estudiem separació en la codificació canal font, transmissió no codificada i dues tècniques de codificació conjunta de font i canal basades en decodificació conjunta a recepció: NBJD, que no utilitza binning no explicit i decodificació conjunta a recepció i HDA, que comprimeix la font i transmet l?error. Al decodificador, la paraula comprimida es recupera per decodificació conjunta amb l?error transmès i la informació adicional. Extenem aquestes tècniques a esquemes híbrids analògics-digitals i esquemes multi-capa. Estudiem numèricament el problema i donem resultats per el règim de SNR finita. Proporcionem expresions tancades per el Distortion exponent a regim de alta SNR. ////// Castellà: Consideramos el problema de codificación conjunta de fuente y canal de enviar una fuente Gaussiana sobre un canal fading multi-antena (MIMO) cuando el decodificador tiene información adicional correlada con la fuente, con una cualidad también variante en el tiempo. Asumimos un modelo block fading para ambas calidades del canal y la información adicional. Asumimos conocimiento perfecto de canal en recepción, mientras que el transmisor solo dispone de conocimiento estadístico. Estamos interesados en la distorsión cuadrática media de este sistema. Estudiamos separación en la codificación canal fuente, transmisión no codificada y dos técnicas de codificación conjunta de fuente y canal basadas en decodificación conjunta en recepción: NBJD, que no utiliza binning no explicito y decodificación conjunta, y HDA, que comprime la fuente y transmite el error. Al decodificar, la palabra comprimida es recuperada por decodificación conjunta entre el error transmitido y la información adicional. Extendemos estas técnicas a esquemas híbridos analógico-digitales y esquemas multi-capa. Estudiamos numéricamente el problema y damos resultados para el régimen de SNR finita. Proporcionamos expresiones cerradas para el Distortion exponent en régimen de alta SNR ////// English: We consider the joint source-channel coding problem of sending a Gaussian source over a multiple input-multiple output (MIMO) fading channel when the decoder has additional correlated side information whose quality is also time-varying. We assume a block fading model for both the channel and side information qualities, and assume perfect state information at the receiver, while the transmitter has only a statistical knowledge. We are interested in the expected squared-error distortion for this system. We study separate source-channel coding, uncoded transmission and two joint source-channel transmission schemes based on joint decoding at the receiver: NBJD, that uses no explicit binning and joint decoding of the side information and the channel output at the decoder and HDA, that compresses the source and transmits the error. At the decoder, the quantized codeword is recovered by means of joint decoding of the error and the side information. We extend such techniques to hybrid digital-analog and multi-layer schemes. We study numerically the problem and give results in the finite SNR regime. We provide closed form expressions for the distortion exponent in the high SNR regime

Capacity of a Class of State-Dependent Orthogonal Relay Channels

Abstract-The class of orthogonal relay channels in which the orthogonal channels connecting the source terminal to the relay and the destination, and the relay to the destination, depend on a state sequence, is considered. It is assumed that the state sequence is fully known at the destination while it is not known at the source or the relay. The capacity of this class of relay channels is characterized, and shown to be achieved by the partial decode-compress-and-forward (pDCF) scheme. Then the capacity of certain binary and Gaussian state-dependent orthogonal relay channels are studied in detail, and it is shown that the compress-and-forward (CF) and partial-decode-andforward (pDF) schemes are suboptimal in general. To the best of our knowledge, this is the first single relay channel model for which the capacity is achieved by pDCF, while pDF and CF schemes are both suboptimal. Furthermore, it is shown that the capacity of the considered class of state-dependent orthogonal relay channels is in general below the cut-set bound. The conditions under which pDF or CF suffices to meet the cut-set bound, and hence, achieve the capacity, are also derived