On information rates over a binary input channel

We study communication systems over band-limited Additive White Gaussian Noise (AWGN) channels in which the transmitter output is constrained to be symmetric binary (bi-polar). In this work we improve the original Ozarov-Wyner-Ziv (OWZ) lower bound on capacity by introducing a new achievability scheme with two advantages over the studied OWZ scheme which is based on peak-power constrained pulse-amplitude modulation. Our scheme achieves a moderately improved information rate and it does so with much less sign transitions of the binary signal. The gap between the known upper-bound based on spectral constrains of bi-polar signals and our achievable lower bound is reduced to 0.86 bits per Nyquist interval at high SNR.

The Filtered Gaussian Primitive Diamond Channel

We investigate the special case of diamond relay comprising a Gaussian channel with identical frequency response between the user and the relays and fronthaul links with limited rate from the relays to the destination. We use the oblivious compress and forward (CF) with distributed compression and decode and forward (DF) where each relay decodes the whole message and sends half of its bits to the destination. We derive achievable rate by using time-sharing between DF and CF. The optimal time sharing proportion between DF and CF and power and rate allocations are different at each frequency and are fully determined.

On sparse sensing and sparse sampling of coded signals at sub-Landau rates

Advances of information-theoretic understanding of sparse sampling of continuous uncoded signals at sampling rates exceeding the Landau rate were reported in recent works. This work examines sparse sampling of coded signals at sub-Landau sampling rates. It is shown that with coded signals the Landau condition may be relaxed and the sampling rate required for signal reconstruction and for support detection can be lower than the effective bandwidth. Equivalently, the number of measurements in the corresponding sparse sensing problem can be smaller than the support size. Tight bounds on information rates and on signal and support detection performance are derived for the Gaussian sparsely sampled channel and for the frequency-sparse channel using the context of state dependent channels. Support detection results are verified by a simulation. When the system is high-dimensional the required SNR is shown to be finite but high and rising with decreasing sampling rate, in some practical applications it can be lowered by reducing the a-priory uncertainty about the support e.g. by concentrating the frequency support into a finite number of subbands.

Scaling Laws and Techniques in Decentralized Processing of Interfered Gaussian Channels

The scaling laws of the achievable communication rates and the corresponding upper bounds of distributed reception in the presence of an interfering signal are investigated. The scheme includes one transmitter communicating to a remote destination via two relays, which forward messages to the remote destination through reliable links with finite capacities. The relays receive the transmission along with some unknown interference. We focus on three common settings for distributed reception, wherein the scaling laws of the capacity (the pre-log as the power of the transmitter and the interference are taken to infinity) are completely characterized. It is shown in most cases that in order to overcome the interference, a definite amount of information about the interference needs to be forwarded along with the desired message, to the destination. It is exemplified in one scenario that the cut-set upper bound is strictly loose. The results are derived using the cut-set along with a new bounding technique, which relies on multi letter expressions. Furthermore, lattices are found to be a useful communication technique in this setting, and are used to characterize the scaling laws of achievable rates.

On Extrinsic Information of Good Codes Operating Over Discrete Memoryless Channels

We show that the Extrinsic Information about the coded bits of any good (capacity achieving) code operating over a wide class of discrete memoryless channels (DMC) is zero when channel capacity is below the code rate and positive constant otherwise, that is, the Extrinsic Information Transfer (EXIT) chart is a step function of channel quality, for any capacity achieving code. It follows that, for a common class of iterative receivers where the error correcting decoder must operate at first iteration at rate above capacity (such as in turbo equalization, turbo channel estimation, parallel and serial concatenated coding and the like), classical good codes which achieve capacity over the DMC are not effective and should be replaced by different new ones. Another meaning of the results is that a good code operating at rate above channel capacity falls apart into its individual transmitted symbols in the sense that all the information about a coded transmitted symbol is contained in the corresponding received symbol and no information about it can be inferred from the other received symbols. The binary input additive white Gaussian noise channel is treated in part 1 of this report. Part 2 extends the results to the symmetric binary channel and to the binary erasure channel and provides an heuristic extension to wider class of channel models.