Convolutional Codes in Rank Metric with Application to Random Network Coding

Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to create dependencies between the different shots, particular convolutional codes in rank metric are used. These codes are so-called (partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one. First, distance measures for convolutional codes in rank metric are shown and two constructions of (P)UM codes in rank metric based on the generator matrices of maximum rank distance codes are presented. Second, an efficient error-erasure decoding algorithm for these codes is presented. Its guaranteed decoding radius is derived and its complexity is bounded. Finally, it is shown how to apply these codes for error correction in random linear and affine network coding.Comment: presented in part at Netcod 2012, submitted to IEEE Transactions on Information Theor

Telemetering and telecommunications research

The New Mexico State University (NMSU) Center for Space Telemetering and Telecommunications systems is engaged in advanced communications systems research. Four areas of study that are being sponsored concern investigations into the use of trellis-coded modulation (TCM). In particular, two areas concentrate on carrier synchronization research in TCM M-ary phase shift key (MPSK) systems. A third research topic is the study of interference effects on TCM, while the fourth research area is in the field of concatenated TCM systems

On the Universality of Spatially Coupled LDPC Codes over Intersymbol Interference Channels

In this paper, we derive the exact input/output transfer functions of the optimal a-posteriori probability channel detector for a general ISI channel with erasures. Considering three channel impulse responses of different memory as an example, we compute the BP and MAP thresholds for regular spatially coupled LDPC codes with joint iterative detection and decoding. When we compare the results with the thresholds of ISI channels with Gaussian noise we observe an apparent inconsistency, i.e., a channel which performs better with erasures performs worse with AWGN. We show that this anomaly can be resolved by looking at the thresholds from an entropy perspective. We finally show that with spatial coupling we can achieve the symmetric information rates of different ISI channels using the same code

Error control techniques for satellite and space communications

The performance of bandwidth efficient trellis inner codes using two-dimensional MPSK signal constellations in a NASA concatenated coding is summarized. Work was also continued on trellis coded modulation using multi-dimensional signal sets. Achievable lower bounds on free distance trellis codes were proved and the existence of good trellis coded modulation (TCM) schemes were established for a variety of signal constellations. The performance of TCM schemes on fading channels is being investigated. Preliminary results indicate that bandwidth efficient trellis coding is feasible on such channels, but that the important design parameter is no longer the minimum free Euclidean distance

Multiple accessing for the collision channel without feedback

Bibliography: p. 582."September 1984." Reprinted from IEEE Journal on Selected Areas in Communications, vol. SAC-2, no.4, July 1984."...National Science Foundation... Grant NSF/ECS-79-19880." "...Advanced Research Project Agency... Grant ONR/N00014-75-C1183."Joseph Y.N. Hui

First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory

This article considers the performance of digital communication systems transmitting messages over finite-state erasure channels with memory. Information bits are protected from channel erasures using error-correcting codes; successful receptions of codewords are acknowledged at the source through instantaneous feedback. The primary focus of this research is on delay-sensitive applications, codes with finite block lengths and, necessarily, non-vanishing probabilities of decoding failure. The contribution of this article is twofold. A methodology to compute the distribution of the time required to empty a buffer is introduced. Based on this distribution, the mean hitting time to an empty queue and delay-violation probabilities for specific thresholds can be computed explicitly. The proposed techniques apply to situations where the transmit buffer contains a predetermined number of information bits at the onset of the data transfer. Furthermore, as additional performance criteria, large deviation principles are obtained for the empirical mean service time and the average packet-transmission time associated with the communication process. This rigorous framework yields a pragmatic methodology to select code rate and block length for the communication unit as functions of the service requirements. Examples motivated by practical systems are provided to further illustrate the applicability of these techniques.Comment: To appear in IEEE Transactions on Information Theor

Minimality for puncturing convolutional codes

This paper investigates encoders optimization for the Hamming weight after periodic puncturing, and discusses minimality issues that may affect the performance of the punctured encoders. Periodically puncturing a minimal encoder produces a higher rate encoder that may or may not be minimal. If it is not minimal, it may have a zero-output loop and it may be catastrophic. A code search can use a fast algorithm to determine whether an encoder's state diagram has a zero-output loop under periodic symbol puncturing, and a proposed method to assess the performance of codes with a zero-output loop that are not catastrophic. As an example, the paper optimizes rate-1/4 unpunctured codes for Hamming weight under both bit-wise and symbol-wise periodic puncturing. Code tables and simulation results are included