Continue to Site

Welcome to

Welcome to our site! is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

[SOLVED] Hard Vs LLR demodulation of QAM symbols

Not open for further replies.


Member level 2
Jul 24, 2010
Reaction score
Trophy points
Activity points
Hi, we know that optimum demodulation of QAM symbols is based on decision regions obtained from MAP rule: argmax(p(Sm|r)) where Sm is any possible sent symbol and r is the received symbol.

Now what is the difference between hard and LLR demodulation ?? Which one is based on above ??
Thanks in advance.

As far as I know, the above rule is called hard decision detection (decoding), because the output of the detector is a valid symbol, which is the final decision. In soft decision, usually a two parallel (or serial) convolution codes are concatenated in a certain way to make these codewords look like independent. At the receiver there are two serial soft-input soft output Veterbi algorithm detectors the exchange soft information between each other, until a saturation point reached. This is called soft decoding and its performance is much better than hard decoding. Turbo codes class is an example of this.

This is independent of coding. what is the difference between hard and LLR demodulation of QAM symbols ?? Which one is based on MAP rule ? Assuming equiprobable symbols MAP rule reduces to finding the minimum Euclidean distance.

I found the answer. Hard decoding is based on minimum Euclidean distance. This gives the optimum estimate of SYMBOLS. But in LLR demodulation BITS are estimated NOT symbols. LLR gives a reliability measure for each estimated bit. The bigger this number, the more precise the estimate. One major use of this is in decoding of M-ary modulated convolutional codes where by assignment of reference reliability factors to 1 and 0 of trellis branches, the metrics can be calculated.

Not open for further replies.

Part and Inventory Search

Welcome to