Non Binary Low Density Parity Check Codes Decoding Over Galois Field

Yogita Ahuja, Ramesh Bharti

Conventional LDPC codes have a low decoding complexity but may have high encoding complexity. The encoding complexity is typically of the order O(n2)[5]. Also high storage space may be required to explicitly store the generator matrix. For long block  lengths the storage space required would be huge. The above factors make the implementation of the Conventional LDPC codes less attractive.

These codes are usually decoded using the sum-product algorithm, which is a  message passing algorithm working on the Tanner graph of the code[5]. The sparseness of the parity check matrix is essential for attaining good performance with sum-product decoding. The time complexity of the sum- product algorithm is linear in code length. This property makes it possible to implement a practical decoder for long lengths.