Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work,  introduce an efficient algorithm to find all stopping sets, of size less than some threshold, of a fixed low-density parity-check (LDPC) matrix. The solution is inspired by the algorithm proposed by Rosnes and Ytrehus in 2005 to find an exhaustive list of all small-size turbo stopping sets in a turbo code. The efficiency of the proposed algorithm is demonstrated by several numerical examples. For instance,  have applied the algorithm to the ll-known (3, 5)-regular (155, 64) Tanner code and found all stopping sets of size at most 18 in about 1 min on a standard desktop computer. Also,  have verified that the minimum stopping set size of the (4896, 2474) Ramanujan-Margulis code is indeed 24, and that the corresponding multiplicity is exactly 204. Furthermore,  have applied the algorithm to the IEEE 802.16e LDPC codes and determined the minimum stopping set size and the corresponding multiplicity exactly for these codes. Finally, as an application,  present a greedy algorithm to find a small number of redundant parity checks to add to the original parity-check matrix in order to remove all stopping sets in the corresponding Tanner graph of size less than the minimum distance. An extensive case study of the (155, 64) Tanner code illustrates the usefulness of the algorithm, and  present a 110 times 155 redundant parity-check matrix for this code with no stopping sets of size less than the minimum distance. Simulation results of iterative decoding on the binary erasure channel show performance improvements for low-to-medium erasure probabilities when this redundant parity-check matrix is used for decoding.
['Eirik Rosnes', 'Øyvind Ytrehus']
I am writing a research paper on a idea An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices
[{"from": "human", "value": "I am writing a research paper on a idea An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work,  introduce an efficient algorithm to find all stopping sets, of size less than some threshold, of a fixed low-density parity-check (LDPC) matrix. The solution is inspired by the algorithm proposed by Rosnes and Ytrehus in 2005 to find an exhaustive list of all small-size turbo stopping sets in a turbo code. The efficiency of the proposed algorithm is demonstrated by several numerical examples. For instance,  have applied the algorithm to the ll-known (3, 5)-regular (155, 64) Tanner code and found all stopping sets of size at most 18 in about 1 min on a standard desktop computer. Also,  have verified that the minimum stopping set size of the (4896, 2474) Ramanujan-Margulis code is indeed 24, and that the corresponding multiplicity is exactly 204. Furthermore,  have applied the algorithm to the IEEE 802.16e LDPC codes and determined the minimum stopping set size and the corresponding multiplicity exactly for these codes. Finally, as an application,  present a greedy algorithm to find a small number of redundant parity checks to add to the original parity-check matrix in order to remove all stopping sets in the corresponding Tanner graph of size less than the minimum distance. An extensive case study of the (155, 64) Tanner code illustrates the usefulness of the algorithm, and  present a 110 times 155 redundant parity-check matrix for this code with no stopping sets of size less than the minimum distance. Simulation results of iterative decoding on the binary erasure channel show performance improvements for low-to-medium erasure probabilities when this redundant parity-check matrix is used for decoding."}]