On the capacity of multisource non-coherent network coding

We consider multisource non-coherent network coding, where multiple sources send information to one or multiple receivers. We prove that this is equivalent to a ldquosubspacerdquo channel, that takes subspaces as inputs and outputs. We then show that the rate of each individual receiver is upper bounded as deltai(T - delta1 - delta2), where deltai is what we define to be the ldquodominatingrdquo dimension in the subspace codebook of source i, and T is the ldquocoherencerdquo time of the network

End-to-End Error-Correcting Codes on Networks with Worst-Case Symbol Errors

The problem of coding for networks experiencing worst-case symbol errors is considered. We argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting schemes can be arbitrarily far from achieving the optimal network throughput. A new transform metric for errors under the considered model is proposed. Using this metric, we replicate many of the classical results from coding theory. Specifically, we prove new Hamming-type, Plotkin-type, and Elias-Bassalygo-type upper bounds on the network capacity. A commensurate lower bound is shown based on Gilbert-Varshamov-type codes for error-correction. The GV codes used to attain the lower bound can be non-coherent, that is, they do not require prior knowledge of the network topology. We also propose a computationally-efficient concatenation scheme. The rate achieved by our concatenated codes is characterized by a Zyablov-type lower bound. We provide a generalized minimum-distance decoding algorithm which decodes up to half the minimum distance of the concatenated codes. The end-to-end nature of our design enables our codes to be overlaid on the classical distributed random linear network codes [1]. Furthermore, the potentially intensive computation at internal nodes for the link-by-link error-correction is un-necessary based on our design.Comment: Submitted for publication. arXiv admin note: substantial text overlap with arXiv:1108.239

Performance Analysis of Physical Layer Network Coding.

Network coding has emerged as an innovative approach to network operation that can significantly enhance network throughput. The key goal of this thesis is to understand fundamental aspects of physical layer network coding, where network coding is performed at the physical layer. As a simple but typical example of network coding, we consider a network scenario where two users transmit messages through a common channel and the receiver reconstructs the exclusive-or of the two messages. For this channel, we investigate the error exponent which can provide guidelines for the design of e±cient communication systems using network coding. From a practical point of view, we examine the performance of channel codes for this problem. Assuming that each user transmits data using the same low-density parity-check (LDPC) code and each link is an additive white Gaussian noise channel, we evaluate the noise thresholds of LDPC codes via density evolution methods. Other important issues considered in this thesis are related to transmission over fading channels. First, we study the performance of LDPC codes over non-ergodic fading channels. In non-ergodic channels, reliable communication at a constant rate is impossible. Assuming that the fading coe±cient is randomly chosen but fixed during transmission of an LDPC codeword, we derive the outage probability of LDPC-coded systems. We also propose an accurate frequency domain channel estimator based on the Slepian basis expansion. The proposed scheme operates with high accuracy requiring only the knowledge of the maximum delay spread of the channel. Finally, we investigate the capacity achieving input of non-coherent Rayleigh fading channels taking into account power constraints imposed by a non-linear power amplifier. We show that the optimal input is discrete with finite support which indicates that capacity can be computed using finite dimensional optimization.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64791/1/jinhokim_1.pd

Rate regions for coherent and noncoherent multisource network error correction

In this paper we derive capacity regions for network error correction with both known and unknown topologies (coherent and non-coherent network coding) under a multiple-source multicast transmission scenario. For the multiple-source non-multicast scenario, given any achievable network code for the error-free case, we construct a code with a reduced rate region for the case with errors

Dispensing with channel estimation: differentially modulated cooperative wireless communications

As a benefit of bypassing the potentially excessive complexity and yet inaccurate channel estimation, differentially encoded modulation in conjunction with low-complexity noncoherent detection constitutes a viable candidate for user-cooperative systems, where estimating all the links by the relays is unrealistic. In order to stimulate further research on differentially modulated cooperative systems, a number of fundamental challenges encountered in their practical implementations are addressed, including the time-variant-channel-induced performance erosion, flexible cooperative protocol designs, resource allocation as well as its high-spectral-efficiency transceiver design. Our investigations demonstrate the quantitative benefits of cooperative wireless networks both from a pure capacity perspective as well as from a practical system design perspective

Code-rate-optimized differentially modulated near-capacity cooperation

It is widely recognized that half-duplex-relay-aided differential decode-and-forward (DDF) cooperative transmission schemes are capable of achieving a cooperative diversity gain, while circumventing the potentially excessive-complexity and yet inaccurate channel estimation, especially in mobile environments. However, when a cooperative wireless communication system is designed to approach the maximum achievable spectral efficiency by taking the cooperation-induced multiplexing loss into account, it is not obvious whether or not the relay-aided system becomes superior to its direct-transmission based counterpart, especially, when advanced channel coding techniques are employed. Furthermore, the optimization of the transmit-interval durations required by the source and relay is an open issue, which has not been well understood in the context of half-duplex relaying schemes. Hence, we first find the optimum transmission duration, which is proportional to the adaptive channel-code rate of the source and relay in the context of Code-Rate-Optimized (CRO) TDMA-based DDF-aided half-duplex systems for the sake of maximizing the achievable network throughput. Then, we investigate the benefits of introducing cooperative mechanisms into wireless networks, which may be approached in the context of the proposed CRO cooperative system both from a pure capacity perspective and from the practical perspective of approaching the Discrete-input Continuous-output Memoryless Channel (DCMC) capacity with the aid of the proposed Irregular Distributed Differential (IrDD) coding aided scheme. In order to achieve a near-capacity performance at a low-complexity, an adaptive-window-duration based Multiple-Symbol Differential Sphere Detection (MSDSD) scheme is employed in the iterative detection aided receiver. Specifically, upon using the proposed near-capacity system design, the IrDD coding scheme devised becomes capable of performing within about 1.8 dB from the corresponding single-relay-aided DDF cooperative system’s DCMC capacity