9 research outputs found
One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation
Low complexity decoding algorithms are necessary to meet data rate
requirements in excess of 1 Tbps. In this paper, we study one and two bit
message passing algorithms for belief propagation decoding of low-density
parity-check (LDPC) codes and analyze them by density evolution. The variable
nodes (VNs) exploit soft information from the channel output. To decrease the
data flow, the messages exchanged between check nodes (CNs) and VNs are
represented by one or two bits. The newly proposed quaternary message passing
(QMP) algorithm is compared asymptotically and in finite length simulations to
binary message passing (BMP) and ternary message passing (TMP) for spectrally
efficient communication with higher-order modulation and probabilistic
amplitude shaping (PAS). To showcase the potential for high throughput forward
error correction, spatially coupled LDPC codes and a target spectral efficiency
(SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are
observed compared to BMP and TMP, respectively. The gap to unquantized belief
propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates,
the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in
the considered example.Comment: Accepted for IEEE/OSA Journal on Lightwave Technolog
One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation
Low complexity decoding algorithms are necessary to meet data rate requirements in excess of 1 Tbps. In this paper, we study one and two bit message passing algorithms for belief propagation decoding of low-density parity-check (LDPC) codes and analyze them by density evolution. The variable nodes (VNs) exploit soft information from the channel output. To decrease the data flow, the messages exchanged between check nodes (CNs) and VNs are represented by one or two bits. The newly proposed quaternary message passing (QMP) algorithm is compared asymptotically and in finite length simulations to binary message passing (BMP) and ternary message passing (TMP) for spectrally efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS). To showcase the potential for high throughput forward error correction, spatially coupled LDPC codes and a target spectral efficiency (SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates, the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in the considered example
Novel High-Throughput Decoding Algorithms for Product and Staircase Codes based on Error-and-Erasure Decoding
Product codes (PCs) and staircase codes (SCCs) are conventionally decoded
based on bounded distance decoding (BDD) of the component codes and iterating
between row and column decoders. The performance of iterative BDD (iBDD) can be
improved using soft-aided (hybrid) algorithms. Among these, iBDD with combined
reliability (iBDD-CR) has been recently proposed for PCs, yielding sizeable
performance gains at the expense of a minor increase in complexity compared to
iBDD. In this paper, we first extend iBDD-CR to SCCs. We then propose two novel
decoding algorithms for PCs and SCCs which improve upon iBDD-CR. The new
algorithms use an extra decoding attempt based on error and erasure decoding of
the component codes. The proposed algorithms require only the exchange of hard
messages between component decoders, making them an attractive solution for
ultra high-throughput fiber-optic systems. Simulation results show that our
algorithms based on two decoding attempts achieve gains of up to dB for
both PCs and SCCs. This corresponds to a optical reach enhancement over
iBDD with bit-interleaved coded modulation using quadrature amplitude
modulation
A Soft-Aided Staircase Decoder Using Three-Level Channel Reliabilities
The soft-aided bit-marking (SABM) algorithm is based on the idea of marking
bits as highly reliable bits (HRBs), highly unreliable bits (HUBs), and
uncertain bits to improve the performance of hard-decision (HD) decoders. The
HRBs and HUBs are used to assist the HD decoders to prevent miscorrections and
to decode those originally uncorrectable cases via bit flipping (BF),
respectively. In this paper, an improved SABM algorithm (called iSABM) is
proposed for staircase codes (SCCs). Similar to the SABM, iSABM marks bits with
the help of channel reliabilities, i.e., using the absolute values of the
log-likelihood ratios. The improvements offered by iSABM include: (i) HUBs
being classified using a reliability threshold, (ii) BF randomly selecting
HUBs, and (iii) soft-aided decoding over multiple SCC blocks. The decoding
complexity of iSABM is comparable of that of SABM. This is due to the fact that
on the one hand no sorting is required (lower complexity) because of the use of
a threshold for HUBs, while on the other hand multiple SCC blocks use soft
information (higher complexity). Additional gains of up to 0.53 dB with respect
to SABM and 0.91 dB with respect to standard SCC decoding at a bit error rate
of are reported. Furthermore, it is shown that using 1-bit
reliability marking, i.e., only having HRBs and HUBs, only causes a gain
penalty of up to 0.25 dB with a significantly reduced memory requirement
Refined Reliability Combining for Binary Message Passing Decoding of Product Codes
We propose a novel soft-aided iterative decoding algorithm for product codes
(PCs). The proposed algorithm, named iterative bounded distance decoding with
combined reliability (iBDD-CR), enhances the conventional iterative bounded
distance decoding (iBDD) of PCs by exploiting some level of soft information.
In particular, iBDD-CR can be seen as a modification of iBDD where the hard
decisions of the row and column decoders are made based on a reliability
estimate of the BDD outputs. The reliability estimates are derived using
extrinsic message passing for generalized low-density-parity check (GLDPC)
ensembles, which encompass PCs. We perform a density evolution analysis of
iBDD-CR for transmission over the additive white Gaussian noise channel for the
GLDPC ensemble. We consider both binary transmission and bit-interleaved coded
modulation with quadrature amplitude modulation.We show that iBDD-CR achieves
performance gains up to dB compared to iBDD with the same internal
decoder data flow. This makes the algorithm an attractive solution for very
high-throughput applications such as fiber-optic communications