mohatta2015.pdf

THE IDEA 155
detected value. Thus, the signed soft value would be +428. Similarly, the signed
soft value for s 2 would be +640.
The approach just described is optimistic, in that it implicitly assumes the other
detected symbol values are correct. This is why we only change one symbol value.
More accurate soft information can be obtained by defining the second sequence
metric as the best metric corresponding to the set of possible sequences for which
52 is opposite to its detected value.
What we're really doing is approximating the MAPSD approach for soft information
generation with the MLSD metrics. Specifically, we are assuming that for
the set of sequences for which the s 2 is the detected value, the detected sequence
dominates. Similarly, for the set of sequences for which s^ is not the detected
value, one sequence dominates. This notion of considering only dominant terms
when forming soft information is referred to as dual maxima or simply dual-max.
7.1.2.3 Coding In general, some form of forward error correction (FEC) encoding
is used to protect the message symbols. One way to achieve this is to send additional
symbols that are functions of the message symbols. This adds extra information
or redundancy to the packet, which can be used to correct symbol errors during
the decoding process. Coding is also used for forward error detection (FED). In
general, some codes are designed for FEC and some for FED. However, they need
not be used the way they were intended to be used.
A simple example of a code for either FEC or FED is a parity check code. In
the Alice and Bob example, we sent two symbols, si and s 2 . We could send a third
symbol, S3 = S1S2· First, suppose the coding is used for FED. At the receiver, we
would check whether S3 is equal to S1I2· If not, an error would be declared. (One
way to handle such an error is to have the packet sent a second time.) Second,
suppose the coding is used for FEC. At the receiver, we would use r\, r 2 and
r.-j to form soft information. For example, suppose the MMSE linear equalization
decision variables have values z\ — —0.18914, 22 = 0.26488, and Z3 = 0.16822.
In the decoding process, we would form message metrics for each possible metric.
For example, message 1 has si = +1 and s 2 = —1· The parity symbol would be
53 = (+1)(—1) = —1. The message metric would be (+l)«i + (—1)22 + ( — 1)^3,
which equals —0.622246. For messages 2 and 3, the message metrics would be
0.092477 and 0.243956. We would declare the third message the detected message
as it has the largest message metric.
7.1.3 Joint demodulation and decoding
With MLSD and MAPSD, we take advantage of the fact that the symbols can only
take on the values +1 and —1. There is further signal structure that we can use
to our advantage. We can use the fact that there are a finite number of possible
messages or packet values. All symbol sequences are not possible.
The best way to use this information would be to perform maximum likelihood
packet detection (MLPD). Like MLSD, we consider all possible packet values (a
subset of all possible symbol sequences) and form a metric for each one. The
packet with the best metric is the detected packet value or message.