Security gap analysis of some LDPC coded transmission schemes over the flat and fast fading Gaussian wire-tap channels

n/

Nested turbo codes for the costa problem

Driven by applications in data-hiding, MIMO broadcast channel coding, precoding for interference cancellation, and transmitter cooperation in wireless networks, Costa coding has lately become a very active research area. In this paper, we first offer code design guidelines in terms of source- channel coding for algebraic binning. We then address practical code design based on nested lattice codes and propose nested turbo codes using turbo-like trellis-coded quantization (TCQ) for source coding and turbo trellis-coded modulation (TTCM) for channel coding. Compared to TCQ, turbo-like TCQ offers structural similarity between the source and channel coding components, leading to more efficient nesting with TTCM and better source coding performance. Due to the difference in effective dimensionality between turbo-like TCQ and TTCM, there is a performance tradeoff between these two components when they are nested together, meaning that the performance of turbo-like TCQ worsens as the TTCM code becomes stronger and vice versa. Optimization of this performance tradeoff leads to our code design that outperforms existing TCQ/TCM and TCQ/TTCM constructions and exhibits a gap of 0.94, 1.42 and 2.65 dB to the Costa capacity at 2.0, 1.0, and 0.5 bits/sample, respectively

Information-theoretic Physical Layer Security for Satellite Channels

Shannon introduced the classic model of a cryptosystem in 1949, where Eve has access to an identical copy of the cyphertext that Alice sends to Bob. Shannon defined perfect secrecy to be the case when the mutual information between the plaintext and the cyphertext is zero. Perfect secrecy is motivated by error-free transmission and requires that Bob and Alice share a secret key. Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the Shannon model assuming that the channels are noisy and proved that secrecy can be achieved without sharing a secret key. This model is called wiretap channel model and secrecy capacity is known when Eve's channel is noisier than Bob's channel. In this paper we review the concept of wiretap coding from the satellite channel viewpoint. We also review subsequently introduced stronger secrecy levels which can be numerically quantified and are keyless unconditionally secure under certain assumptions. We introduce the general construction of wiretap coding and analyse its applicability for a typical satellite channel. From our analysis we discuss the potential of keyless information theoretic physical layer security for satellite channels based on wiretap coding. We also identify system design implications for enabling simultaneous operation with additional information theoretic security protocols

Performance Analysis and Design of Two Edge Type LDPC Codes for the BEC Wiretap Channel

We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a code construction method using two edge type LDPC codes based on the coset encoding scheme. Using a standard LDPC ensemble with a given threshold over the BEC, we give a construction for a two edge type LDPC ensemble with the same threshold. If the given standard LDPC ensemble has degree two variable nodes, our construction gives rise to degree one variable nodes in the code used over the main channel. This results in zero threshold over the main channel. In order to circumvent this problem, we numerically optimize the degree distribution of the two edge type LDPC ensemble. We find that the resulting ensembles are able to perform close to the boundary of the rate-equivocation region of the wiretap channel. There are two performance criteria for a coding scheme used over a wiretap channel: reliability and secrecy. The reliability measure corresponds to the probability of decoding error for the intended receiver. This can be easily measured using density evolution recursion. However, it is more challenging to characterize secrecy, corresponding to the equivocation of the message for the wiretapper. M\'easson, Montanari, and Urbanke have shown how the equivocation can be measured for a broad range of standard LDPC ensembles for transmission over the BEC under the point-to-point setup. By generalizing the method of M\'easson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how the equivocation for the wiretapper can be computed. We find that relatively simple constructions give very good secrecy performance and are close to the secrecy capacity. However finding explicit sequences of two edge type LDPC ensembles which achieve secrecy capacity is a more difficult problem. We pose it as an interesting open problem.Comment: submitted to IEEE Transactions on Information Theory. Updated versio

Fundamental Finite Key Limits for One-Way Information Reconciliation in Quantum Key Distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that one-way information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during information reconciliation is not generally valid. We propose an improved approximation that takes into account finite key effects and numerically test it against codes for two probability distributions, that we call binary-binary and binary-Gaussian, that typically appear in quantum key distribution protocols