Multi-rate control over AWGN channels via analog joint source-channel coding

We consider the problem of controlling an unstable plant over an additive white Gaussian noise (AWGN) channel with a transmit power constraint, where the signaling rate of communication is larger than the sampling rate (for generating observations and applying control inputs) of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and which is often much lower than the rate that can be communicated. This setting offers the opportunity of improving the system performance by employing multiple channel uses to convey a single message (output plant observation or control input). Common ways of doing so are through either repeating the message, or by quantizing it to a number of bits and then transmitting a channel coded version of the bits whose length is commensurate with the number of channel uses per sampled message. We argue that such “separated source and channel coding” can be suboptimal and propose to perform joint source-channel coding. Since the block length is short we obviate the need to go to the digital domain altogether and instead consider analog joint source-channel coding. For the case where the communication signaling rate is twice the sampling rate, we employ the Archimedean bi-spiral-based Shannon-Kotel'nikov analog maps to show significant improvement in stability margins and linear-quadratic Gaussian (LQG) costs over simple schemes that employ repetition

Multi-rate control over AWGN channels via analog joint source-channel coding

We consider the problem of controlling an unstable plant over an additive white Gaussian noise (AWGN) channel with a transmit power constraint, where the signaling rate of communication is larger than the sampling rate (for generating observations and applying control inputs) of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and which is often much lower than the rate that can be communicated. This setting offers the opportunity of improving the system performance by employing multiple channel uses to convey a single message (output plant observation or control input). Common ways of doing so are through either repeating the message, or by quantizing it to a number of bits and then transmitting a channel coded version of the bits whose length is commensurate with the number of channel uses per sampled message. We argue that such “separated source and channel coding” can be suboptimal and propose to perform joint source-channel coding. Since the block length is short we obviate the need to go to the digital domain altogether and instead consider analog joint source-channel coding. For the case where the communication signaling rate is twice the sampling rate, we employ the Archimedean bi-spiral-based Shannon-Kotel'nikov analog maps to show significant improvement in stability margins and linear-quadratic Gaussian (LQG) costs over simple schemes that employ repetition

Multi-rate control over AWGN channels via analog joint source-channel coding

We consider the problem of controlling an unstable plant over an additive white Gaussian noise (AWGN) channel with a transmit power constraint, where the signaling rate of communication is larger than the sampling rate (for generating observations and applying control inputs) of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and which is often much lower than the rate that can be communicated. This setting offers the opportunity of improving the system performance by employing multiple channel uses to convey a single message (output plant observation or control input). Common ways of doing so are through either repeating the message, or by quantizing it to a number of bits and then transmitting a channel coded version of the bits whose length is commensurate with the number of channel uses per sampled message. We argue that such “separated source and channel coding” can be suboptimal and propose to perform joint source-channel coding. Since the block length is short we obviate the need to go to the digital domain altogether and instead consider analog joint source-channel coding. For the case where the communication signaling rate is twice the sampling rate, we employ the Archimedean bi-spiral-based Shannon-Kotel'nikov analog maps to show significant improvement in stability margins and linear-quadratic Gaussian (LQG) costs over simple schemes that employ repetition

Joint Unitary Triangularization for MIMO Networks

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio

Cooperative network-coding system for wireless sensor networks

Describes a cooperative network coding system for wireless sensor networks. In this paper, we propose two practical power) and bandwidth)efficient systems based on amplify)and)forward (AF) and decode)and)forward (DF) schemes to address the problem of information exchange via a relay. The key idea is to channel encode each source’s message by using a high)performance non)binary turbo code based on Partial Unit Memory (PUM) codes to enhance the bit)error)rate performance, then reduce the energy consumption and increase spectrum efficiency by using network coding (NC) to combine individual nodes’ messages at the relay before forwarding to the destination. Two simple and low complexity physical layer NC schemes are proposed based on combinations of received source messages at the relay. We also present the theoretical limits and numerical analysis of the proposed schemes. Simulation results under Additive White Gaussian Noise, confirm that the proposed schemes achieve significant bandwidth savings and fewer transmissions over the benchmark systems which do not resort to NC. Theoretical limits for capacity and Signal to Noise Ratio behaviour for the proposed schemes are derived. The paper also proposes a cooperative strategy that is useful when insufficient combined messages are received at a node to recover the desired source messages, thus enabling the system to retrieve all packets with significantly fewer retransmission request messages

Compute-and-Forward: Harnessing Interference through Structured Codes

Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure