## 2 Basic Concepts and Work Scope
### Data Aggregation Domains, Side Information, and Analogy to Communications Systems  
We are interested in exploiting spatial side information in the fingerprint domain before mapping the fingerprints to an estimated position. It is argued that aggregating the positions in the position domain will result in accumulating the errors introduced by the pattern-matching method for each position estimate in the aggregation stage. In contrast, aggregating the fingerprints in the fingerprint domain would result in processing raw data, with more information, before calculating the position estimates using the pattern-matching method.  
The reasoning stated above is analogous to the estimation of transmitted bits in a communications system, using so-called hard-bits and soft-bits (as a result of implementing hard-decision or soft-decision decoding) [77; 78].  
Let us focus for a while on the receiver side of a communications system implementing digital amplitude modulation. As one possibility, the receiver can work with hard-bits. Hard-bits result from quantizing analog information in the demodulator from each received symbol into bits with ultimately one of two possible states (0 or 1). Assuming that the transmitted bits are encoded, these hard-bits are then post-processed in a decoding stage to obtain an estimation of the transmitted bits. With this approach, the quantization removes information that otherwise would have helped the decoder to reduce the decoding error and to ultimately produce a better estimate of the transmitted bits.  
Alternatively, the receiver can work in the decoding stage with raw information or soft-bits, that is, analog information from each received bit expressed as a real number, prior to the quantization stage. This last approach is beneficial for retaining as much information as possible from the received symbols or bits during the decoding phase. It is particularly implemented with error correction codes designed to exploit information from adjacent bits, such as convolutional codes or turbo codes, and complemented with a suitable decoder that makes use of this side information. The decoder ultimately outputs the estimated transmitted bits as real numbers for posterior quantization.  
Now, we can make an analogy in which the pattern-matching method in our positioning system would be analogous to the quantizer of a receiver, and the aggregation of data (fingerprints or positions) in our positioning system would be analogous to what occurs in the decoder of a receiver (Figure 8).  
More specifically, the first case (hard-bits), depicted as _Case 1_ in Figure 8, associates the following analogies. A quantizer (or a demodulator fulfilling this function) quantizing the received bits or symbols into hard-bits (without exploiting the side information) is analogous to a pattern-matching method estimating the positions without exploiting side information. A decoder working with hard-bits is analogous to posterior aggregation, in the position domain, of the estimated positions output by the pattern-matching-method to produce a final position estimate. Then, the second case (soft-bits), depicted as _Case 2_ in Figure 8, associates the following analogies. A decoder exploiting the side information from soft-bits (from the received symbols) is analogous to the aggregation of the fingerprints in the fingerprint domain. A quantizer quantizing (or, more specifically, rounding to 0 or 1 at this stage) decoded soft-bits into hard-bits is analogous to a pattern-matching method estimating the positions with the side information in the fingerprint domain.  
It is shown later that aggregating the side information in the fingerprint domain results in a better performance in terms of minimizing the positioning error than aggregating independent position estimates in the position domain.