# Exact definition of soft bits in digital receiver

At which stage of digital receiver, the bits are considered as soft bits?

I am unable to find the exact definition. I have rough idea how soft bits are different from hard bits but in terms of signal processing, I am confused. The signal after demodulation, phase/frequency/timing offset correction before the hard bits should be considered as soft bits?

I believe adding the samples amplitude of a single bit and averaging it over the number of samples to normalize the amplitude of single bit can be referred as soft bit right before converting it into hard bit?

Soft bits or more generally speaking, soft metrics, are usually taken at the output of the demodulator (e.g. the output of a matched filter sampled at $T_b$). A soft bit can be therefore a real value, but it is usually quantified (which is required if a DSP comes after).

A hard bit is obtained by performing a hard decision on a soft metric. So for instance, if $x[kT_b]$ is the output of the matched filter when a BPSK signal is applied, then a hard-bit can be obtained by simply comparing $x[kTb]>0$, which is $0$ or $1$.

This figure from wikipedia is self-explanatory.

As you see, the output of the matched filter is actually a continuous signal. Some part of your receiver (which is not included in the figure) must perform also timing estimation in order to determine at which instant the output of the matched filter must be sampled. Those samples are the red points in the figure, and might be considered as soft bits. So the higher the magnitude of those samples, the more information they provide about what the original transmitted symbol was. That is the advantage of having soft-bits: they don't only tell you what symbol has been probably sent, they also give an idea about that probability.

• Thanks for the answer. I understand the idea but if the input data is sampled at $T_b$, the data seems barely digital so I normalized it for whole bit duration. Is that correct to do so? Is it possible to explain that visually? – Rok Dec 3 '15 at 10:35
• It is the output of the matched filter that is sampled at $T_b$, not the input data. You don't need to normalise that sample. Actually the greater it is, the better. In fact, when you said "adding the samples amplitude of a single bit and averaging it (...)", you are not far from the idea of what a matched filter actually does. I will update my answer to be more clear. – vaz Dec 3 '15 at 11:06

Soft symbols are used e.g. between a symbol demapper and a decoder.

The symbol demapper basically says "symbol X' that I received looks most similar to the ideal symbol X, but because channel noise "corrupted" X and turned it into X' (typically easily observable on a constellation diagram like the one below: red dots are ideal symbols, blue dots actual received symbols), the symbol demapper assigns a likelihood that the received symbol is the one that the symbol demapper says it is.

This is important because the decoder can then make better decisions during decoding, which I guess is intuitively reasonable.