Protograph-Based LDPC Code Design for Shaped Bit-Metric Decoding

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within 0.63dB and 0.69dB of continuous AWGN capacity for a target frame error rate of 1e-3 at spectral efficiencies of 1.38 and 4.25 bits/channel use, respectively.Comment: 9 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1501.0559

Protograph-based Quasi-Cyclic MDPC Codes for McEliece Cryptosystems

In this paper, ensembles of quasi-cyclic moderate-density parity-check (MDPC) codes based on protographs are introduced and analyzed in the context of a McEliece-like cryptosystem. The proposed ensembles significantly improve the error correction capability of the regular MDPC code ensembles that are currently considered for post-quantum cryptosystems without increasing the public key size. The proposed ensembles are analyzed in the asymptotic setting via density evolution, both under the sum-product algorithm and a low-complexity (error-and-erasure) message passing algorithm. The asymptotic analysis is complemented at finite block lengths by Monte Carlo simulations. The enhanced error correction capability remarkably improves the scheme robustness with respect to (known) decoding attacks.Comment: 5 page

Improving the Decoding Threshold of Tailbiting Spatially Coupled LDPC Codes by Energy Shaping

We show how the iterative decoding threshold of tailbiting spatially coupled (SC) low-density parity-check (LDPC) code ensembles can be improved over the binary input additive white Gaussian noise channel by allowing the use of different transmission energies for the codeword bits. We refer to the proposed approach as energy shaping. We focus on the special case where the transmission energy of a bit is selected among two values, and where a contiguous portion of the codeword is transmitted with the largest one. Given these constraints, an optimal energy boosting policy is derived by means of protograph extrinsic information transfer analysis. We show that the threshold of tailbiting SC-LDPC code ensembles can be made close to that of terminated code ensembles while avoiding the rate loss (due to termination). The analysis is complemented by Monte Carlo simulations, which confirm the viability of the approach

Unequal Diversity LDPC Codes for Relay Channels

A novel protograph-based construction of low-density parity-check (LDPC) codes for the relay channel is proposed, which provides an enhanced unequal error protection property named unequal diversity. The focus is on quasi-static fading channels and on the high-code-rate (R>1/2) regimes, for which (according to the Singleton bound) no full diversity can be achieved. In the proposed construction, some nodes (and the corresponding codeword fragment) associated with the code graph enjoy the diversity provided by the relay, whereas the remaining nodes do not experience any diversity. The proposed approach can be thus tailored to transmit information blocks with different priority levels. An extrinsic information transfer (EXIT) analysis is developed, which allows an accurate performance prediction over the considered channel model, and more in general over block-fading channels