PROBLEM FORMULATION
3.1 Problem Statement
Low density parity check codes are forward error correcting codes. The LDPC block codes are inefficient, since a new code must be hypothesized each time a change in frame size is desired. A number of algorithms with varying complexity and performance have been proposed for LDPC decoding. But achieving a balanced trade-off between decoding performance and implementation complexity still remains a potential problem. LDPC decoding algorithms operates by making either hard decision or soft decision on the message received from the noisy channel [20].
3.1.1 Sum product Algorithm
The sum product algorithm for LDPC decoding is a soft decision message passing algorithm. In case of soft decision based algorithms, the input data to the decoder is the channel probabilities, represented in logarithmic ratio which is known as log-likelihood ratio (LLR). This algorithm requires LLR for variable node operations to make decoding decisions. The LLRs are transferred over to the variable nodes (V), this variable node carry out the sum operation on the input LLRs as in equation (1) and computed messages are passed along the connected edges to the check nodes (C).
SPA Variable node operation:
V_i=〖LLR〗_n+∑_(j≠i)▒C_j (1)
Where n=1,2,. . . .number of variable nodes i, j=1,2,. . …show more content…
In this project in order to achieve trade-off between the decoder performance and implementation complexity the message passing algorithm is proposed it is also called as belief propagation algorithm. MPA is reliable compared with other decoding algorithms; it has a complexity only linearly proportional to the check node degree. The check node operation of the MPA consists of a simple parity check operation requiring XOR logic only, as shown in equation