We consider probabilistic network codes over Gaussian relay network from coding theoretic perspective. Network coding by relay nodes is performed based on reliable received signals from source nodes. Effect of the signal selection and the relaying error on the performance is addressed by deriving upper bound on the expected error probability at the destination.

We analyze a coding scheme used in secret key agreement based on noisy resource for physical layer security. We discuss approximate performance bound for a variant of asymmetric Slepian-Wolf coding system, or source coding with side information at the decoder. Numerical results indicate that the derived bound provides accurate prediction of error probability when noisy resource is the binary-input Gaussian channel.

We analyze the error performance of coding scheme that is found in the protocol for secret key agreement based on the Gaussian channel. The approach is regarded as the Slepian-Wolf coding or the source coding with side information at the decoder. One remarkable feature of the coding in the key agreement is that two parties may extract the set of reliable signals before Slepian-Wolf coding is performed. We derive a tight upper bound on the error probability of this coding scheme, which allows us to quantify the effect of signal extraction.

We study the signal sets for information theoretically secure key agreement with public discussion over the Gaussian and flat fading channels. Alice transmits signals to Bob over a noisy channel while Eve receives signals through an independent noisy channel. By utilizing this noisy resource, Alice and Bob wish to share a secret key on which Eve has a negligible amount of information. We present a protocol that allows Alice and Bob to share a common secret information, and encompass the signal sets for an efficient protocol in information theoretic sense.

In this paper, we consider an information theoretically secure cryptographic primitive known as oblivious transfer based on noisy channels. We present a protocol and two approaches to base the primitive on much wider class of signal sets and continuous channels than the existing results on the Gaussian channel. We also evaluate the associated information theoretic efficiency of the protocol for some cases of interest.

We study the coding for nonbinary sources with side information at the decoder. The use of binary linear code and the associated decoding scheme is proposed, with a special emphasis on low-density parity-check codes. With iterative decoding based on the constraint due to the encoding structure, reasonably good performance is achieved when compared with Slepian-Wolf limit.

We study the use of the additive white Gaussian noise channel to achieve oblivious transfer which is an important cryptographic primitive in multiparty computation. An efficient protocol for unconditionally secure oblivious transfer is presented. We show that channel input alphabets with a certain algebraic structure and their partitions are useful in achieving privacy for players and ensuring high efficiency of the protocol. Security and information theoretic efficiency of the protocol is investigated.

It is known that noise on communication channels can be a powerful resource for certain cryptographic purposes, basically by utilizing the randomness to ensure the secrecy. In this paper, we study information theoretically secure key agreement through the use of the additive white Gaussian noise channel and public discussion. We present a protocol for key agreement that defines the computation and communications between the two communicating parties to share a common secret information, about which negligible amount of information is revealed to other third parties. We discuss the signal design, secrecy and the achievable rate of the protocol.

Two cryptographic primitives, commitment and oblivious transfer, are devised based on the additive white Gaussian noise channel and discrete input alphabet. We present protocols and analyze the security and information theoretic efficiencies.

This paper studies (very) high-rate serially concatenated codes employing rate-1 recursive convolutional encoders and Hamming codes. We show that these codes exhibit capacity-approaching performance by the EXIT chart analysis and simulations, and that they outperform many known codes of similar parameters with respect to error rates. The serially concatenated codes can be decoded with (relatively) low complexity, and have large flexibility in code lengths and code rates.

In this paper, we focus on the suboptimality of iterative decoding on graphs with cycles, through examining the use of a reliability-based decoding algorithm for some concatenated codes with an interleaver, known as turbo-like codes. The a posteriori probabilities delivered by the iterative decoding are regarded as reliability information, and an efficient algorithm for the overall linear block code is applied at certain iterations. Simulation results show that the suboptimality of iterative decoding due to cycles can be at least partially compensated by this approach. Some insights about the potential additional coding gains achievable are investigated based on the characteristics of the constituent decoders. These characteristics are related to the nature of suboptimality in the overall iterative decoding. The effects of some code parameters and channel conditions on the behavior of iterative decoding are also studied for a better understanding of its suboptimality.

In this paper, the use of a reliability-based decoding algorithm for some concatenated codes with an interleaver, known as turbo-like codes, is examined to address and overcome the suboptimality of iterative decoding. Simulation results show that the suboptimality of iterative decoding for moderate length codes can be at least partially compensated by this combined approach. Some insights about the potential additional coding gains achievable by the combined approach are investigated based on the characteristics of the constituent decoders, which highlights the nature of suboptimality in iterative decoding.

Iterative decoding of multilevel coded modulation is discussed. Despite its asymptotic optimality with proper design, the error correcting capability of multilevel codes may not be fully exploited for finite block length with conventional multistage decoding. This fact stems from the suboptimality of multistage decoding giving rise to increased error multiplicity at lower index stages and the associated error propagation to higher stages. Such problems can be overcome in many situations by introducing iterative decoding which often significantly compensates the suboptimality of a staged decoder. The class of multilevel codes achieving practically important bit-error performance near the Shannon limit becomes far wider with iterative decoding.

In this paper, multilevel coded asymmetric modulation with multistage decoding and unequal error protection (UEP) is discussed. These results further emphasize the fact that unconventional signal set partitionings are more promising than traditional (Ungerboeck-type) partitionings, to achieve UEP capabilities with multilevel coding and multistage decoding. Three types of unconventional partitionings are analyzed for asymmetric 8-PSK and 16-QAM constellations over the additive white Gaussian noise channel to introduce design guidelines. Generalizations to other PSK and QAM type constellations follow the same lines. Upper bounds on the bit-error probability based on union bound arguments are first derived. In some cases, these bounds become loose due to the large overlappings of decision regions associated with asymmetric constellations and unconventional partitionings. To overcome this problem, simpler and tighter approximated bounds are derived. Based on these bounds, it is shown that additional refinements can be achieved in the construction of multilevel UEP codes, by introducing asymmetries in PSK and QAM signal constellations.