B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

14.9 Soft Decoding 843
modify the hard decoder inputy. Each flip pattern e; consists of ls in bit positions to be flipped
and Os in the remaining bit positions. For each flip pattern e;, construct
c; = hard decision (y J E9 e;
(14.38a)
and compute the corresponding reliability metric
n
M; = Lrj · (2c;J - 1)
)=I
( 15.38b)
The codeword with the maximum M; is the decoded output.
There are three types of Chase algorithm. First, we sort the bit reliability from low to high:
( 14.39)
Type 1 Test all flipping patterns of weight less than or equal to (dmin - 1 ) .
Type 2 Identify the Ldnun/2J least reliable bit positions {i1 i2 · · · ild min /2J }. Test all flipping
patterns of weight less than or equal to Ldnun/2 - lJ .*
Type 3 Test flipping patterns of weight w = 1, 3, ... , dmin - 1 by placing ls in the w least
reliable bit positions.
The block diagram of Chase algorithms is shown in Fig. 14.18. The three Chase algorithms
differ only in how the flipping patterns are generated. In addition, we should note that Chase
decoders can exchange reliability and likelihood information with other receiver units in a joint
effort to improve the decoding performance. From the input end, the set of flipping patterns can
take additional suggestions from other receiver units. From the output end, multiple codeword
candidates, along with their reliability metrics, can be sent to additional decoding units for
further processing and eventual elimination.
Figure 14. 18
Block diagram of
Chase
soft-decoding
algorithms.
(y1, Y2, · · · , Yn)
- I Har _ d _ bit - - -+--<-+--­ Hard
►
---.---- . dec1s10n . rn
decoder
Find least
reliable
positions
Generate
flipping
patterns
cj
Compute
metric
MJ
f------l►l8f-------------- 1
Soft
output
Select
maximum
Hard
output
* The operation L·J is often known as the "floor." In particular, LxJ represents the largest integer less than or
equal to x.