The code design of non-binary low-density parity-check codes for the erasure channel, under maximum a posteriori decoding, is addressed. In particular, a partially structured ensemble of codes, characterized by a careful control of the amount and of the connectivity of the variable nodes of small degrees, is proposed. The identified ensemble of codes is analyzed in terms of asymptotic thresholds and weight distribution and it is shown that codes from the ensemble provide a remarkable trade-off between waterfall performance, error floor, and decoding complexity. As an example, the performance curve of a short (256,128) code on the memoryless 16-ary erasure channel tightly approaches the Singleton bound at least down to a codeword error rate of 10-9, at low decoding complexity.
Garrammone, G., Paolini, E., Matuz, B., Liva, G. (2015). Non-Binary LDPC Erasure Codes with Separated Low-Degree Variable Nodes. IEEE TRANSACTIONS ON COMMUNICATIONS, 63(11), 3937-3949 [10.1109/TCOMM.2015.2468232].
Non-Binary LDPC Erasure Codes with Separated Low-Degree Variable Nodes
PAOLINI, ENRICO;
2015
Abstract
The code design of non-binary low-density parity-check codes for the erasure channel, under maximum a posteriori decoding, is addressed. In particular, a partially structured ensemble of codes, characterized by a careful control of the amount and of the connectivity of the variable nodes of small degrees, is proposed. The identified ensemble of codes is analyzed in terms of asymptotic thresholds and weight distribution and it is shown that codes from the ensemble provide a remarkable trade-off between waterfall performance, error floor, and decoding complexity. As an example, the performance curve of a short (256,128) code on the memoryless 16-ary erasure channel tightly approaches the Singleton bound at least down to a codeword error rate of 10-9, at low decoding complexity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.