NB-LDPC Decoder Simulator

Team: Eric Reiss

Project

  • Modern communication systems require increased reliability and speed to meet the large loads placed upon them.
  • Error correction coding is a method of encoding data in a way that allows the data to be recovered at the receiving end if there is an error during transmission.
  • Low-density parity-check (LDPC) codes are a form of error correction coding that are used in many communication and storage technologies.
  • LDPC codes operate on groups of bits are known as non-binary LDPC (NB-LDPC) codes and may improve communication speed.
  • This project aims to facilitate research into NB-LDPC schemes by developing software that will simulate the hardware of a non-binary LDPC decoder.

System

a wireframe of the system diagram

Methods

  • This simulator was prototyped in Python and implemented using SystemC.
  • The project implements the belief propagation algorithm for a Galois Field size of 2^B.
  • The structure of the NB-LDPC code follows the structure of binary LDPC codes with the parity check matrix entries being replaced by randomly selected elements of the given field.
  • The simulator implements the Belief Propagation algorithm.
  • To reduce the computational complexity, a look-up table was constructed for each check node.
Effect of non-zero parity-check matrix entries

Effect of non-zero parity-check matrix entries

D. Declercqand M. Fossorier, "Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$," in IEEE Transactions on Communications, vol. 55, no. 4

Conclusion

  • This project was successful in informing the author of advances in the field of non-binary LDPC codes.
  • A method of generating a look-up table was created to reduce computational complexity.
  • Unfortunately, the simulator was not completed enough to yield any numerical results, but should be completed in the next month.
  • Future research will focus on implementing novel decoding algorithms and testing them with this simulator.

D. Declercqand M. Fossorier, "Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$," in IEEE Transactions on Communications, vol. 55, no. 4, pp. 633-643, April 2007, doi: 10.1109/TCOMM.2007.894088