Compute-and-Forward: Harnessing Interference through Structured Codes

Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure

Secure Degrees of Freedom for Gaussian Channels with Interference: Structured Codes Outperform Gaussian Signaling

In this work, we prove that a positive secure degree of freedom is achievable for a large class of Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wire-tap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers.Comment: 6 pages, Submitted to IEEE Globecom, March 200

New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes

This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate structured codes with constant column weights 3 and higher. The proposed codes are efficiently encodable and exhibit good structural properties. Experimental results on decoding performance with the sum-product algorithm show that the novel codes offer substantial practical application potential, for instance, in high-speed applications in magnetic recording and optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications

Secure GDoF of the Z-channel with Finite Precision CSIT: How Robust are Structured Codes?

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself -- a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.Comment: 34 pages, 10 figure

INFORMATION THEORETIC SECRET KEY GENERATION: STRUCTURED CODES AND TREE PACKING

This dissertation deals with a multiterminal source model for secret key generation by multiple network terminals with prior and privileged access to a set of correlated signals complemented by public discussion among themselves. Emphasis is placed on a characterization of secret key capacity, i.e., the largest rate of an achievable secret key, and on algorithms for key construction. Various information theoretic security requirements of increasing stringency: weak, strong and perfect secrecy, as well as different types of sources: finite-valued and continuous, are studied. Specifically, three different models are investigated. First, we consider strong secrecy generation for a discrete multiterminal source model. We discover a connection between secret key capacity and a new source coding concept of ``minimum information rate for signal dissemination,'' that is of independent interest in multiterminal data compression. Our main contribution is to show for this discrete model that structured linear codes suffice to generate a strong secret key of the best rate. Second, strong secrecy generation is considered for models with continuous observations, in particular jointly Gaussian signals. In the absence of suitable analogs of source coding notions for the previous discrete model, new techniques are required for a characterization of secret key capacity as well as for the design of algorithms for secret key generation. Our proof of the secret key capacity result, in particular the converse proof, as well as our capacity-achieving algorithms for secret key construction based on structured codes and quantization for a model with two terminals, constitute the two main contributions for this second model. Last, we turn our attention to perfect secrecy generation for fixed signal observation lengths as well as for their asymptotic limits. In contrast with the analysis of the previous two models that relies on probabilistic techniques, perfect secret key generation bears the essence of ``zero-error information theory,'' and accordingly, we rely on mathematical techniques of a combinatorial nature. The model under consideration is the ``Pairwise Independent Network'' (PIN) model in which every pair of terminals share a random binary string, with the strings shared by distinct pairs of terminals being mutually independent. This model, which is motivated by practical aspects of a wireless communication network in which terminals communicate on the same frequency, results in three main contributions. First, the concept of perfect omniscience in data compression leads to a single-letter formula for the perfect secret key capacity of the PIN model; moreover, this capacity is shown to be achieved by linear noninteractive public communication, and coincides with strong secret key capacity. Second, taking advantage of a multigraph representation of the PIN model, we put forth an efficient algorithm for perfect secret key generation based on a combinatorial concept of maximal packing of Steiner trees of the multigraph. When all the terminals seek to share perfect secrecy, the algorithm is shown to achieve capacity. When only a subset of terminals wish to share perfect secrecy, the algorithm is shown to achieve at least half of it. Additionally, we obtain nonasymptotic and asymptotic bounds on the size and rate of the best perfect secret key generated by the algorithm. These bounds are of independent interest from a purely graph theoretic viewpoint as they constitute new estimates for the maximum size and rate of Steiner tree packing of a given multigraph. Third, a particular configuration of the PIN model arises when a lone ``helper'' terminal aids all the other ``user'' terminals generate perfect secrecy. This model has special features that enable us to obtain necessary and sufficient conditions for Steiner tree packing to achieve perfect secret key capacity