The problem of compressing the data transmitted by a number of sensors when the information they are transmitting to some central unit is correlated is considered. A short overview of lattices and their role in communications and signal processing will be given, as well as how they can be applied to the problem of distributed source coding (DSC). The main idea behind DSC is to exploit the existing spatial (or time) correlation among the observations of non-cooperating encoders. Integer-forcing source coding (IFSC) is a specific case of lossy DSC, in which all encoders employ the same nested lattice codebook to code their observations and send them individually to some central decoder. Instead of directly retrieving the individual signals, the decoder first recovers a set of integer linear combinations of those signals and then inverts it to obtain the final estimates within some predefined distortion measure. The central algorithmic problem is the one of finding the appropriate matrix of integer coefficients to obtain the integer linear combinations of the data coming from the sensors that will allow to lower the rates while keeping the same maximum distortion. The problem can be proximally solve using the LLL lattice reduction algorithm to find that integer matrix. An alternative algorithm that returns the exact solution based on the successive minima problem (SMP) is then applied to know the full potential of IFSC. Later on, the IFSC scheme will be tested in a situation where the correlation among the sources belongs to a finite set of possible correlation models, each of which with a given known probability (the so-called semi-blind IFSC). Finally, a very low complexity flavour of IFSC is analysed (so-called one-shot IFSC) that, while having some performance degradation when compared to the results using optimally designed lattices, can probably be the best option to be used in machine-type communication (MTC) devices.

--

Integer forcing source coding

• Electrical Engineering, Electronic Engineering, Information Engineering - Engineering and Technology