You don't have to use LLRs. For example, the sum-product algorithm uses the sum and product of probabilities, rather than the min and sum of LLRs, as in the min-sum algorithm. However, LLRs have the advantage of having a low dynamic range, allowing them to be represented using fixed-point numbers, rather than the more complex floating-point number representation. Also, min and sum calculations are simpler to implement than sum and product calculations. These are the reasons why LLRs are used in the most popular ways of implementing LDPC decoders.

Dear Dileep,

The LLR LDPC decoding is simply the optimum decoder in the sense that it achieves the best possible performance. However , other decoder do exist and the trade off between the complexity and the performance optimization shall be considered. 

Any decoding algorithm can be derived in the probability domain. Moving to the LLR domain is equivalent theoretically but from an implementation viewpoint (in both hardware and software) the LLR domain becomes more robust with respect to numerical issues.

Soft-decision LDPC needs LLRs. However, hard-decision LDPC does not need LLRs.  Soft-decision LDPC use LLR as the initial input information of LDPC decoder. The decoding process of soft-decision LDPC is an iterative process, e.g., min-sum algorithm.

Soft decision LLRs are much more preferable not only due to the robustness of the decoder and ease of handling, but also in the network designing. In case you wish to move on to cooperative communications, you will realise that the properties of LLRs can be very much beneficial in the design and optimisation process. In general there is a underline understanding that "Soft is better than Hard", but this is not always true!

Min sum approximation