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Fig. 4. Original signal (black) compared with a DPCM-compressed signal.
Transmitted samples are marked with red squares.

obtained by xˆ = Ψsˆ . However, some parameters can be directly
estimated in the compressed domain and do not require signal
reconstruction [15]. By working on compressed measurements, smartphone workload can be kept at a reasonable level.

Predictive Algorithms
In compression based on predictive algorithms, the smartphone acting as data concentrator unit implements a virtual
sensor that creates a prediction of the quantity associated to
the process monitored by a certain sensor. When the difference
between the actual value and its prediction exceeds a pre-set
threshold, updates are sent by the wearable node to the central
unit to allow virtual sensor recalibration-thus guaranteeing
zero-latency. Prediction error for the generic sample x(tn) is
computed as ε ( tn ) = x ( tn ) − x ( tn ) where x ( tn ) is the predicted
value provided by the virtual sensor. Error is encoded and
transmitted only when it exceeds a given threshold: ε ( tn ) > δ ,
that can be defined on the basis of a-priori knowledge about the
monitored process and data acquisition system specifications.
An example is reported in Fig. 4. Square marks represent
the samples x(tn) for which the corresponding error ε ( tn )
results are greater than the threshold δ and give rise to a transmission. At the receiver, the signal is simply reconstructed by
means of a zero-order hold. This approach only requires the
storage of a single sample in the wearable device memory.

Compression by Data Encoding
The use of predictive algorithms allows further reduction of
data by the application of suitable encoding schemes. A zerolatency compression algorithm, specifically designed for
WBSNs, is presented in [16]. It employs in sequence a lossy
compression stage based on differential pulse code modulation
(DPCM), as illustrated in Fig. 4, followed by lossless compression based on a variant of Golomb code, which associates
more frequent symbols to shorter codes. The first step allows
the system to reduce the amount of data packets that a sensor
node needs to send, and the second step further reduces payload size in packets.
The output of an analog-to-digital converter (ADC) with B
bit resolution takes values from a finite alphabet of size 2B.
The transmission of the prediction error rather than full samples allows further compression. In fact, although in principle
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prediction error takes values from an alphabet of cardinality
2B+1, actual values fall within a much more limited range for
band-limited signals.
An efficient coding scheme based on modified Golomb
codes is considered [16]. Whereas in traditional Golomb codes
both prefix and suffix have variable length, the variant employs a constant-length suffix, whose size is dictated only by
ADC resolution.
This method allows packet payload size to be losslessly reduced. It can achieve significant compression ratios
for physiological signals and presents some advantages,
namely: a flexible combination between lossy and lossless
stages, that can be modified simply by setting the threshold
value; and a guaranteed zero latency for a reconstruction error not exceeding δ, which is associated to the predicted value
generated by the virtual sensor. The main limitation is a consequence of the correlation between the signal derivative and
the frequency of packet transmission that is higher when the
signal has greater variability. This produces packet bursts,
adversely affecting the optimal use of sensor resources. For
instance, energy harvesting modules might be unable to
fully restore battery or supercapacitor charge, and network
congestion might occur if sensor signals are significantly
correlated.

Lossless Compression for Multiple Sensors
In some biomedical applications, even very small signal variations can convey important information. In these cases, it
is important to completely recover the original information,
acquired by the sensors, after the reconstruction of the compressed signal by using a lossless compression algorithm.
Lossless algorithms usually aim at reducing the sample size,
i.e., the number of bits required for representing a given
sample.
On the other hand, recent applications tend to integrate
multiple sensors-physiological, environmental and inertial-within a single wearable device. This leads to the
problem of the compression of data vector, where a single acquisition combines samples obtained from different sensors.
The solution proposed in [17] consists of two steps: in the first,
a predictive approach is adopted to calculate, for each signal,
the residue between the original one and the predicted value
provided by a very simple predictor. This step allows the data
acquisition system to obtain auxiliary signals characterized
by comparable statistical properties, whereas signals are produced by heterogeneous sensors, corresponding to different
physical processes, and therefore characterized by very different statistical properties, particularly when a programmable
gain amplifier (PGA) is used to adapt the input signal dynamic
range to the converter.
In the second step, a vector coding scheme based on a modified Golomb code [17], which makes use of the definition of
union sets (Fig. 5), is employed for compressing the values of
residues. In this way, all of the codewords that refer to a given
acquisition can be represented with the same prefix, obtaining
under some assumptions a satisfactory compression gain. This

IEEE Instrumentation & Measurement Magazine

June 2020

Instrumentation & Measurement Magazine 23-4

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