Syndrome-Based Encoding of Compressible Sources for M2M Communication

Data originating from many devices and sensors can be modeled as sparse signals. Hence, efficient compression techniques of such data are essential to reduce bandwidth and transmission power, especially for energy constrained devices within machine to machine communication scenarios. This paper provides accurate analysis of the operational distortion-rate function (ODR) for syndrome-based source encoders of noisy sparse sources. We derive the probability density function of error due to both quantization and pre- quantization noise for a type of mixed distributed source comprising Bernoulli and an arbitrary continuous distribution, e.g., Bernoulli- uniform sources. Then, we derive the ODR for two encoding schemes based on the syndromes of Reed-Solomon (RS) and Bose, Chaudhuri, and Hocquenghem (BCH) codes. The presented analysis allows designing a quantizer such that a target average distortion is achieved. As confirmed by numerical results, the closed-form expression for ODR perfectly coincides with the simulation. Also, the performance loss compared to an entropy based encoder is tolerable.