Practical Encoder and Decoder for Power Constrained QC LDPC-Lattice Codes

Khodaiemehr, Hassan; Sadeghi, Mohammad‐Reza; Sakzad, Amin

doi:10.1109/tcomm.2016.2633343

Cited by 34 publications

(37 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, to achieve better performances, we provide a deep neural network decoder for such lattices constructed based on Construction A. Using the same notation proposed in [11] and the deep neural network decoder presented in Section III, we present the lattice decoding algorithm.…”

Section: Deep Learning Methods To Decode Latticesmentioning

confidence: 99%

“…, −1). If the noise n is distributed as a normal distribution N (0, σ 2 ) with zero mean and variance σ 2 , then the transmitted vectors are of the form y = c+4z+n, [11]. At the first step, z has to be decoded.…”

Section: Deep Learning Methods To Decode Latticesmentioning

confidence: 99%

“…Now we define a i = y i − 4ẑ i , for 1 ≤ i ≤ n, and putâ i = 2 − a i for a i > 1 and a i itself otherwise. Similar to [11], we need to define the i-th input LLRs as…”

mentioning

confidence: 99%

“…For VNR = 3 and 6, we let α = 0.1 and β = 0.001 and 5 × (10) −5 , respectively. An error performance comparison for BW 8 between SPA in [11] and our proposed decoding algorithm with four iterations is shown in Fig. 4.…”

mentioning

confidence: 99%

See 3 more Smart Citations

A Neural Network Lattice Decoding Algorithm

Sadeghi

Amirzade

Panario

et al. 2018

2018 IEEE Information Theory Workshop (ITW)

Self Cite

View full text Add to dashboard Cite

Neural network decoding algorithms are recently introduced by Nachmani et al. to decode high-density paritycheck (HDPC) codes. In contrast with iterative decoding algorithms such as sum-product or min-sum algorithms in which the weight of each edge is set to 1, in the neural network decoding algorithms, the weight of every edge depends on its impact in the transmitted codeword. In this paper, we provide a novel feed-forward neural network lattice decoding algorithm suitable to decode lattices constructed based on Construction A, whose underlying codes have HDPC matrices. We first establish the concept of feed-forward neural network for HDPC codes and improve their decoding algorithms compared to Nachmani et al. We then apply our proposed decoder for a Construction A lattice with HDPC underlying code, for which the well-known iterative decoding algorithms show poor performances. The main advantage of our proposed algorithm is that instead of assigning and training weights for all edges, which turns out to be timeconsuming especially for high-density parity-check matrices, we concentrate on edges which are present in most of 4-cycles and removing them gives a girth-6 Tanner graph. This approach, by slight modifications using updated LLRs instead of initial ones, simultaneously accelerates the training process and improves the error performance of our proposed decoding algorithm.

show abstract

Section: Deep Learning Methods To Decode Latticesmentioning

confidence: 99%

Section: Deep Learning Methods To Decode Latticesmentioning

confidence: 99%

“…Now we define a i = y i − 4ẑ i , for 1 ≤ i ≤ n, and putâ i = 2 − a i for a i > 1 and a i itself otherwise. Similar to [11], we need to define the i-th input LLRs as…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A Neural Network Lattice Decoding Algorithm

Sadeghi

Amirzade

Panario

et al. 2018

2018 IEEE Information Theory Workshop (ITW)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Now consider the n-th check node with degree j + 2, according to (27), (28) and the Tanner graph in Fig. 3, the parity-check equation at the n-th check node is (z a n ⊕ g a n ) ⊕ · · · ⊕ (z a n +j n −1 ⊕ g a n +j n −1 )⊕…”

Section: Tanner Graphmentioning

confidence: 99%

On the design of multi-dimensional irregular repeat-accumulate lattice codes

Qiu

Yang

Xie

et al. 2017

2017 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

Most multi-dimensional (more than two dimensions) lattice partitions only form additive quotient groups and lack multiplication operations. This prevents us from constructing lattice codes based on multi-dimensional lattice partitions directly from non-binary linear codes over finite fields. In this paper, we design lattice codes from Construction A lattices where the underlying linear codes are non-binary irregular repeataccumulate (IRA) codes. Most importantly, our codes are based on multi-dimensional lattice partitions with finite constellations. We propose a novel encoding structure that adds randomly generated lattice sequences to the encoder's messages, instead of multiplying lattice sequences to the encoder's messages. We prove that our approach can ensure that the decoder's messages exhibit permutation-invariance and symmetry properties. With these two properties, the densities of the messages in the iterative decoder can be modeled by Gaussian distributions described by a single parameter. With Gaussian approximation, extrinsic information transfer (EXIT) charts for our multi-dimensional IRA lattice codes are developed and used for analyzing the convergence behavior and optimizing the decoding thresholds. Simulation results show that our codes can approach the unrestricted Shannon limit within 0.46 dB and outperform the previously designed lattice codes with two-dimensional lattice partitions and existing lattice coding schemes for large codeword length.

show abstract