| Title | Coding Theorem for Systematic LDGM Codes Under List Decoding |
| Publication Type | Conference Paper |
| Year of Publication | 2018 |
| Authors | Lin, W., Cai, S., Wei, B., Ma, X. |
| Conference Name | 2018 IEEE Information Theory Workshop (ITW) |
| Date Published | nov |
| Keywords | binary-input output symmetric memoryless channels, BIOS Security, Bit error rate, capacity-achieving, capacity-achieving codes, capacity-approaching, channel capacity, channel coding, coding theorem, concatenated code, concatenated codes, Decoding, ensembles, error statistics, frame error rate, Generators, Human Behavior, iterative belief propagation decoding algorithm, iterative decoding, linear codes, list decoding, low density generator matrix (LDGM) codes, Metrics, negligible rate loss, parity check codes, pubcrawl, Resiliency, Scalability, Sparse matrices, spatial coupling, systematic LDGM codes, systematic low density generator matrix codes |
| Abstract | This paper is concerned with three ensembles of systematic low density generator matrix (LDGM) codes, all of which were provably capacity-achieving in terms of bit error rate (BER). This, however, does not necessarily imply that they achieve the capacity in terms of frame error rate (FER), as seen from a counterexample constructed in this paper. We then show that the first and second ensembles are capacity-achieving under list decoding over binary-input output symmetric (BIOS) memoryless channels. We point out that, in principle, the equivocation due to list decoding can be removed with negligible rate loss by the use of the concatenated codes. Simulation results show that the considered convolutional (spatially-coupled) LDGM code is capacity-approaching with an iterative belief propagation decoding algorithm. |
| DOI | 10.1109/ITW.2018.8613510 |
| Citation Key | lin_coding_2018 |
Coding Theorem for Systematic LDGM Codes Under List Decoding