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

Abstract

Abstract-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 higherorder 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 et al. analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called hard decision decoder which, however, exploits 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 et al., binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiberoptic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.

Low-complexity decoding of LDPC codes using reduced-set WBF-based algorithms

“…In this section, we compare WBF-based and reduced-set (RS) decoders in terms of computational complexity and the probability of error. In the simulations, we use (3,6) and (4, 32)-regular LDPC codes with rates 1 2 and 7 8 , respectively. The parity-check matrix for the (3, 6)-regular code is constructed with the progressive edge growth (PEG) method [28].…”

“…Plotted in Fig. 3 is L in the RS decoder versus SNR for the (3,6) and (4, 32)-regular LDPC codes with codeword length 10000 and 8176, respectively. Average number of flipping function calculations obtained by Monte-Carlo simulation for single-bit and multi-bit WBF-based decoders, along with the upper bound of (24) are shown in this figure.…”

“…At low SNRs, neither decoding algorithms are able to correct the errors, so the decoding process continues until the predefined maximum number of iterations is reached, Fig. 3 L versus SNR for the (3,6) and (4,32)-regular LDPC codes with N = 10000 and 8176, respectively and thus the average number of flipping function calculations is the same for singlebit and multi-bit WBF decoders. At intermediate SNRs, the convergence speed of the multi-bit decoding algorithm is higher (i.e., the average number of required iterations is smaller), and therefore, the average number of flipping function calculations for the multibit decoder is lower.…”

“…6, 7, 8, and 9. In these figures, regular (3,6) and (4, 32) LDPC codes with codeword length 10000 and 8176 are employed. In Fig.…”

“…The error performance of BF decoding is inferior to that of the BP, but it is faster and much easier to implement [1,4,5]. Moreover, hard-decoding methods like BF are the only option in some applications, such as high-throughput power fiber-optic communications [6,7], NAND storage systems [8,9], and McEliece cryptosystem [10],due to hardware limitations.…”