Probabilistically-Shaped Coded Modulation with Hard Decision Decoding for Coherent Optical Systems

We consider probabilistic shaping to maximize the achievable information rate of coded modulation (CM) with hard decision decoding. The proposed scheme using binary staircase codes outperforms its uniform CM counterpart by more than 1.3 dB for 64-QAM and 5 bits/symbol

Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially-coupled GLDPC codes with BCH component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on Information Theor

Bit error performance of diffuse indoor optical wireless channel pulse position modulation system employing artificial neural networks for channel equalisation

The bit-error rate (BER) performance of a pulse position modulation (PPM) scheme for non-line-of-sight indoor optical links employing channel equalisation based on the artificial neural network (ANN) is reported. Channel equalisation is achieved by training a multilayer perceptrons ANN. A comparative study of the unequalised `soft' decision decoding and the `hard' decision decoding along with the neural equalised `soft' decision decoding is presented for different bit resolutions for optical channels with different delay spread. We show that the unequalised `hard' decision decoding performs the worst for all values of normalised delayed spread, becoming impractical beyond a normalised delayed spread of 0.6. However, `soft' decision decoding with/without equalisation displays relatively improved performance for all values of the delay spread. The study shows that for a highly diffuse channel, the signal-to-noise ratio requirement to achieve a BER of 10−5 for the ANN-based equaliser is ~10 dB lower compared with the unequalised `soft' decoding for 16-PPM at a data rate of 155 Mbps. Our results indicate that for all range of delay spread, neural network equalisation is an effective tool of mitigating the inter-symbol interference

Achievable Information Rates for Coded Modulation with Hard Decision Decoding for Coherent Fiber-Optic Systems

We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga \emph{et al.} analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called \emph{hard decision decoder} which, however, exploits \emph{soft information} of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As a result, contrary to the conclusion by Liga \emph{et al.}, binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

On Decoding Schemes for the MDPC-McEliece Cryptosystem

Recently, it has been shown how McEliece public-key cryptosystems based on moderate-density parity-check (MDPC) codes allow for very compact keys compared to variants based on other code families. In this paper, classical (iterative) decoding schemes for MPDC codes are considered. The algorithms are analyzed with respect to their error-correction capability as well as their resilience against a recently proposed reaction-based key-recovery attack on a variant of the MDPC-McEliece cryptosystem by Guo, Johansson and Stankovski (GJS). New message-passing decoding algorithms are presented and analyzed. Two proposed decoding algorithms have an improved error-correction performance compared to existing hard-decision decoding schemes and are resilient against the GJS reaction-based attack for an appropriate choice of the algorithm's parameters. Finally, a modified belief propagation decoding algorithm that is resilient against the GJS reaction-based attack is presented