  This paper presents a novel strategy to decentralize the soft detection
procedure in an uplink cell-free massive multiple-input-multiple-output
network. We propose efficient approaches to compute the a posteriori
probability-per-bit, exactly or approximately when having a sequential
fronthaul. More precisely, each access point (AP) in the network computes
partial sufficient statistics locally, fuses it with received partial
statistics from another AP, and then forwards the result to the next AP. Once
the sufficient statistics reach the central processing unit, it performs the
soft demodulation by computing the log-likelihood ratio (LLR) per bit, and then
a channel decoding algorithm (e.g., a Turbo decoder) is utilized to decode the
bits. We derive the distributed computation of LLR analytically.
