Search

Encoding and channel convolution and the corresponding equalization and decoding are a serial concatenation. One might consider the solution to be iterative equalization and decoding in a Turbo fashion. We are showing that it is not necessary to run LDPC decoding and equalization as separate entities in a Turbo manner, but integrate decision-feedback equalization (DFE) directly into the LDPC decoder, performing DFE-like operations as part of the LDPC message passing.

The reciprocity of the channel transfer functions between legitimate users changing randomly delivers the common randomness used in physical-layer key generation. Time-Division Duplexing (TDD) provides this symmetry of the bidirectional channel measurements, despite of uncorrelated noise on both sides and possible hardware imperfections. We now show that also Frequency-Division Duplexing (FDD) yields a usable symmetry as far as the direction of arrival is concerned. Even in wireline communications, be it over power lines or twisted pairs, transfer and far-end crosstalk functions provide useful symmetries, where especially key generation for power line communication may become important for IoT applications.

Belief propagation decoding of binary LDPC codes combines three independent probability estimates, a-priori, intrinsic, and extrinsic information, iterations along the Tanner graph are estimating the value of the received bits, the likelihood of the values increasing with each iteration. The a-priori estimate of the information bits is a measure of the source statistics for generating bit values 0 and 1 (mapped to ±1), reflecting bias and redundancy in the information sequence itself. In this paper, we have modified the a-priori estimate to incorporate memory properties present in the transmitted information sequence resulting from a Markov source. We consider two principle alternatives for decoding. The first option is to use the Markov dependencies directly as further links between variable nodes in the Tanner graph of the LDPC code. The second alternative is to see the Markov source and the LDPC code as a serial concatenation asking for a Turbo iterative decoding between the two corresponding decoders. The latter comes with significant complexity compared to the direct embedding into the LDPC Tanner graph. Especially, one modification applying Jensen’s inequality leads to a very low decoding complexity at no performance loss. The Turbo scheme’s performance depends on the scheduling. Superior performance can be achieved with sufficient iterations in the LDPC decoder itself.

In this paper, we investigate signal space diversity (SSD) of lattice codes to mitigate the effect of impulse noise in wireless MIMO systems. A Middleton Class-A (MCA) model is one of the most accepted models for impulsive interference superimposed to additive white Gaussian noise (AWGN). To prove SSD for both Raleigh fading and impulse noise, we evaluate the pairwise-error probability (PEP) of optimum lattice decoding under perfect knowledge of noise states. However, due to the spatial coupling of impulse noise, the extension of the MCA model to MIMO systems leads to a correlated multivariate distribution. To maintain the full diversity advantages of lattice coding in MIMO systems, we investigate a diagonal design of lattice space-time (ST) coding for Rayleigh fading and correlated impulse noise. We also utilize a null space of the MIMO channel to extract noise states using a simple threshold detector. We show that the optimum lattice ST decoder can be realized by a noise-whitening transformation followed by a conventional sphere decoder. Finally, we evaluate the PEP of the optimum lattice ST decoding, which shows how impulse noise coupling limits the performance improvements of SSD with respect to the number of receive antennas.

We propose a multi-level CSI quantization and key reconciliation scheme for physical layer security. The noisy wireless channel estimates obtained by the users first run through a transformation, prior to the quantization step. This enables the definition of guard bands around the quantization boundaries, tailored for a specific efficiency and not compromising the uniformity required at the output of the quantizer. Our construction results in an better key disagreement and initial key generation rate trade-off when compared to other level-crossing quantization methods.