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We formulate maximum likelihood (ML) channel decoding as a quadratic unconstraint binary optimization (QUBO) and simulate the decoding by the current commercial quantum annealing machine, D-Wave 2000Q. We prepared two implementations with Ising model formulations, generated from the generator matrix and the parity-check matrix respectively. We evaluated these implementations of ML decoding for low-density parity-check (LDPC) codes, analyzing the number of spins and connections and comparing the decoding performance with belief propagation (BP) decoding and brute-force ML decoding with classical computers. The results show that these implementations are superior to BP decoding in relatively short length codes, and while the performance in the long length codes deteriorates, the implementation from the parity-check matrix formulation still works up to 1k length with fewer spins and connections than that of the generator matrix formulation due to the sparseness of parity-check matrices of LDPC.
CA-Polar codes have been selected for all control channel communications in 5G NR, but accurate, computationally feasible decoders are still subject to development. Here we report the performance of a recently proposed class of optimally precise Maxi
Raptor codes have been widely used in many multimedia broadcast/multicast applications. However, our understanding of Raptor codes is still incomplete due to the insufficient amount of theoretical work on the performance analysis of Raptor codes, par
We study the problem of characterizing when two memoryless binary asymmetric channels, described by their transition probabilities $(p,q)$ and $(p,q)$, are equivalent from the point of view of maximum likelihood decoding (MLD) when restricted to $n$-
A complexity-adaptive tree search algorithm is proposed for $boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive cancellation
A low-complexity tree search approach is presented that achieves the maximum-likelihood (ML) decoding performance of Reed-Muller (RM) codes. The proposed approach generates a bit-flipping tree that is traversed to find the ML decoding result by perfo