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Register a new userGeneralized Nearest Neighbor Decoding
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Added by
Wenyi Zhang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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It is well known that for linear Gaussian channels, a nearest neighbor decoding rule, which seeks the minimum Euclidean distance between a codeword and the received channel output vector, is the maximum likelihood solution and hence capacity-achieving. Nearest neighbor decoding remains a convenient and yet mismatched solution for general channels, and the key message of this paper is that the performance of the nearest neighbor decoding can be improved by generalizing its decoding metric to incorporate channel state dependent output processing and codeword scaling. Using generalized mutual information, which is a lower bound to the mismatched capacity under independent and identically distributed codebook ensemble, as the performance measure, this paper establishes the optimal generalized nearest neighbor decoding rule, under Gaussian channel input. Several suboptimal but reduced-complexity generalized nearest neighbor decoding rules are also derived and compared with existing solutions. The results are illustrated through several case studies for channels with nonlinear effects, and fading channels with receiver channel state information or with pilot-assisted training.
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Information transmission over a multiple-input-multiple-output (MIMO) fading channel with imperfect channel state information (CSI) is investigated, under a new receiver architecture which combines the recently proposed generalized nearest neighbor decoding rule (GNNDR) and a successive procedure in the spirit of successive interference cancellation (SIC). Recognizing that the channel input-output relationship is a nonlinear mapping under imperfect CSI, the GNNDR is capable of extracting the information embedded in the joint observation of channel output and imperfect CSI more efficiently than the conventional linear scheme, as revealed by our achievable rate analysis via generalized mutual information (GMI). Numerical results indicate that the proposed scheme achieves performance close to the channel capacity with perfect CSI, and significantly outperforms the conventional pilot-assisted scheme, which first estimates the CSI and then uses the estimated CSI as the true one for coherent decoding.
Generalized Goppa codes are defined by a code locator set $mathcal{L}$ of polynomials and a Goppa polynomial $G(x)$. When the degree of all code locator polynomials in $mathcal{L}$ is one, generalized Goppa codes are classical Goppa codes. In this work, binary generalized Goppa codes are investigated. First, a parity-check matrix for these codes with code locators of any degree is derived. A careful selection of the code locators leads to a lower bound on the minimum Hamming distance of generalized Goppa codes which improves upon previously known bounds. A quadratic-time decoding algorithm is presented which can decode errors up to half of the minimum distance. Interleaved generalized Goppa codes are introduced and a joint decoding algorithm is presented which can decode errors beyond half the minimum distance with high probability. Finally, some code parameters and how they apply to the Classic McEliece post-quantum cryptosystem are shown.
We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric. The proposed algorithm closes half of the gap between conventional iterative bounded distance decoding (iBDD) and turbo product decoding based on the Chase--Pyndiah algorithm, at the expense of some increase in complexity. Furthermore, the proposed algorithm entails only a limited increase in data flow compared to iBDD.
We study a noncoherent multiple-input multiple-output (MIMO) fading multiple-access channel (MAC), where the transmitters and the receiver are aware of the statistics of the fading, but not of its realisation. We analyse the rate region that is achievable with nearest neighbour decoding and pilot-assisted channel estimation and determine the corresponding pre-log region, which is defined as the limiting ratio of the rate region to the logarithm of the SNR as the SNR tends to infinity.
We study the information rates of non-coherent, stationary, Gaussian, multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbour decoding and pilot-aided channel estimation. In particular, we analyse the behaviour of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity. We demonstrate that nearest neighbour decoding and pilot-aided channel estimation achieves the capacity pre-log - which is defined as the limiting ratio of the capacity to the logarithm of SNR as the SNR tends to infinity - of non-coherent multiple-input single-output (MISO) flat-fading channels, and it achieves the best so far known lower bound on the capacity pre-log of non-coherent MIMO flat-fading channels.
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