Toward one Symbol Network Coding Vectors

In this paper, we propose a novel design for network coding vectors that limits the overhead information. Network coding vectors contain information regarding the operations the packets have undergone in the network nodes. They are used at the decoder side to invert coding operations and recover the data. We propose to reduce the size of this side information with the use of Vandermonde-like generator matrices at the sources. These matrices permit to describe the coding operations performed on packets with only one symbol. We analytically investigate the limitations arising from such design constraints. Interestingly, we find that the feasible generation size is upper bounded by log_2 q in Galois field mathbb{F}_q of size q as this is the maximum packet diversity allowed by the employed generator matrices. In addition, we show that network coding nodes should only perform addition operations in order to maintain the properties of the coding vectors. We finally discuss the benefits and limitations of the proposed coding vectors in practical systems

Coding with Constraints: Minimum Distance Bounds and Systematic Constructions

We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes with good minimum distance that can be decoded efficiently. On this note, we provide theoretical bounds on the minimum distance of such a code based on the coded symbol constraints. We refine these bounds in the case where we demand a systematic linear code. Finally, we provide conditions under which each of these bounds can be achieved by choosing our code to be a subcode of a Reed-Solomon code, allowing for efficient decoding. This problem has been considered in multisource multicast network error correction. The problem setup is also reminiscent of locally repairable codes.Comment: Submitted to ISIT 201

Mobile Audiovisual Terminal: System Design and Subjective Testing in DECT and UMTS networks

It is anticipated that there will shortly be a requirement for multimedia terminals that operate via mobile communications systems. This paper presents a functional specification for such a terminal operating at 32 kb/s in a digital European cordless telecommunications (DECT) and universal mobile telecommunications system (UMTS) radio network. A terminal has been built, based on a PC with digital signal processor (DSP) boards for audio and video coding and decoding. Speech coding is by a phonetically driven code-excited linear prediction (CELP) speech coder and video coding by a block-oriented hybrid discrete cosine transform (DCT) coder. Separate channel coding is provided for the audio and video data. The paper describes the techniques used for audio and video coding, channel coding, and synchronization. Methods of subjective testing in a DECT network and in a UMTS network are also described. These consisted of subjective tests of first impressions of the mobile audio–visual terminal (MAVT) quality, interactive tests, and the completion of an exit questionnaire. The test results showed that the quality of the audio was sufficiently good for comprehension and the video was sufficiently good for following and repeating simple mechanical tasks. However, the quality of the MAVT was not good enough for general use where high-quality audio and video was needed, especially when transmission was in a noisy radio environment

On Coding for Reliable Communication over Packet Networks

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks.Comment: 33 pages, 6 figures; revised appendi

Network monitoring in multicast networks using network coding

In this paper we show how information contained in robust network codes can be used for passive inference of possible locations of link failures or losses in a network. For distributed randomized network coding, we bound the probability of being able to distinguish among a given set of failure events, and give some experimental results for one and two link failures in randomly generated networks. We also bound the required field size and complexity for designing a robust network code that distinguishes among a given set of failure events

Multilevel Topological Interference Management

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background for this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, a baseline TIM-TIN approach is proposed which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network.Comment: To be presented at 2013 IEEE Information Theory Worksho