Design of Finite-Length Irregular Protograph Codes with Low Error Floors over the Binary-Input AWGN Channel Using Cyclic Liftings

We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.Comment: Submitted to IEEE Trans. Communication

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle $c$ of length $\ell(c)$ in the base graph such that the inverse image of $c$ in the lifted graph consists of only cycles of length strictly larger than $\ell(c)$. The proposed method is universal in the sense that it can be applied to any LDPC code over any channel and for any iterative decoding algorithm. It also preserves important properties of the base code such as degree distributions, encoder and decoder structure, and in some cases, the code rate. The proposed method is applied to both structured and random codes over the binary symmetric channel (BSC). The error floor improves consistently by increasing the lifting degree, and the results show significant improvements in the error floor compared to the base code, a random code of the same degree distribution and block length, and a random lifting of the same degree. Similar improvements are also observed when the codes designed for the BSC are applied to the additive white Gaussian noise (AWGN) channel

A tiny public key scheme based on Niederreiter Cryptosystem

Due to the weakness of public key cryptosystems encounter of quantum computers, the need to provide a solution was emerged. The McEliece cryptosystem and its security equivalent, the Niederreiter cryptosystem, which are based on Goppa codes, are one of the solutions, but they are not practical due to their long key length. Several prior attempts to decrease the length of the public key in code-based cryptosystems involved substituting the Goppa code family with other code families. However, these efforts ultimately proved to be insecure. In 2016, the National Institute of Standards and Technology (NIST) called for proposals from around the world to standardize post-quantum cryptography (PQC) schemes to solve this issue. After receiving of various proposals in this field, the Classic McEliece cryptosystem, as well as the Hamming Quasi-Cyclic (HQC) and Bit Flipping Key Encapsulation (BIKE), chosen as code-based encryption category cryptosystems that successfully progressed to the final stage. This article proposes a method for developing a code-based public key cryptography scheme that is both simple and implementable. The proposed scheme has a much shorter public key length compared to the NIST finalist cryptosystems. The key length for the primary parameters of the McEliece cryptosystem (n=1024, k=524, t=50) ranges from 18 to 500 bits. The security of this system is at least as strong as the security of the Niederreiter cryptosystem. The proposed structure is based on the Niederreiter cryptosystem which exhibits a set of highly advantageous properties that make it a suitable candidate for implementation in all extant systems

Compound Multiple Access Channel with Confidential Messages

In this paper, we study the problem of secret communication over a Compound Multiple Access Channel (MAC). In this channel, we assume that one of the transmitted messages is confidential that is only decoded by its corresponding receiver and kept secret from the other receiver. For this proposed setting (compound MAC with confidential messages), we derive general inner and outer bounds on the secrecy capacity region. Also, as examples, we investigate 'Less noisy' and 'Gaussian' versions of this channel, and extend the results of the discrete memoryless version to these cases. Moreover, providing numerical examples for the Gaussian case, we illustrate the comparison between achievable rate regions of compound MAC and compound MAC with confidential messages.Comment: Accepted at IEEE ICC 2014. arXiv admin note: substantial text overlap with arXiv:1402.479

Binary CEO Problem under Log-Loss with BSC Test-Channel Model

In this paper, we propose an efficient coding scheme for the two-link binary Chief Executive Officer (CEO) problem under logarithmic loss criterion. The exact rate-distortion bound for a two-link binary CEO problem under the logarithmic loss has been obtained by Courtade and Weissman. We propose an encoding scheme based on compound LDGM-LDPC codes to achieve the theoretical bounds. In the proposed encoding, a binary quantizer using LDGM codes and a syndrome-coding employing LDPC codes are applied. An iterative joint decoding is also designed as a fusion center. The proposed CEO decoder is based on the sum-product algorithm and a soft estimator.Comment: 5 pages. arXiv admin note: substantial text overlap with arXiv:1801.0043