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Register a new userDesign of Bilayer and Multi-layer LDPC Ensembles from Individual Degree Distributions
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Added by
Eshed Ram
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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A new approach for designing bilayer and multi-layer LDPC codes is proposed and studied in the asymptotic regime. The ensembles are defined through individual uni-variate degree distributions, one for each layer. We present a construction that: 1) enables low-complexity decoding for high-SNR channel instances, 2) provably approaches capacity for low-SNR instances, 3) scales linearly (in terms of design complexity) in the number of layers. For the setup where decoding the second layer is significantly more costly than the first layer, we propose an optimal-cost decoding schedule and study the trade-off between code rate and decoding cost.
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This paper is focused on the derivation of some universal properties of capacity-approaching low-density parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information-theoretic bounds. These bounds are expressed in terms of the target block/ bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any sub-optimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative and are easy to calculate. Finally, some interesting open problems are considered.
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This paper investigates the design and performance of delayed bit-interleaved coded modulation (DBICM) with low-density parity-check (LDPC) codes. For Gray labeled square $M$-ary quadrature amplitude modulation (QAM) constellations, we investigate the optimal delay scheme with the largest spectrum efficiency of DBICM for a fixed maximum number of delayed time slots and a given signal-to-noise ratio. When analyzing the capacity of DBICM, we find two important properties: the capacity improvement due to delayed coded bits being mapped to the real and imaginary parts of the transmitted symbols are independent of each other; a pair of delay schemes with delayed coded bits having identical bit-channel capacity lead to equivalent DBICM capacity. Using these two properties, we efficiently optimize the delay scheme for any uniform Gray-QAM systems. Furthermore, these two properties enable efficient LDPC code designs regarding unequal error protection via bit-channel type classifications. Moreover, we use protograph-based extrinsic information transfer charts to jointly optimize degree distributions and channel assignments of LDPC codes and propose a constrained progressive edge growth like algorithm to jointly construct LDPC codes and bit-interleavers for DBICM, taking distinctive bit-channels capacity into account. Simulation results demonstrate that the designed LDPC coded DBICM systems significantly outperform LDPC coded BICM systems.
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