Phased burst error-correcting array codes

Various aspects of single-phased burst-error-correcting array codes are explored. These codes are composed of two-dimensional arrays with row and column parities with a diagonally cyclic readout order; they are capable of correcting a single burst error along one diagonal. Optimal codeword sizes are found to have dimensions n1×n2 such that n2 is the smallest prime number larger than n1. These codes are capable of reaching the Singleton bound. A new type of error, approximate errors, is defined; in q-ary applications, these errors cause data to be slightly corrupted and therefore still close to the true data level. Phased burst array codes can be tailored to correct these codes with even higher rates than befor

Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance

The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code. Furthermore, we present a third technique for bounding the minimum Hamming distance based on the embedding of a given repeated-root cyclic code into a repeated-root cyclic product code. A second quadratic-time probabilistic burst error decoding procedure based on the third bound is outlined. Index Terms Bound on the minimum distance, burst error, efficient decoding, folded code, repeated-root cyclic code, repeated-root cyclic product cod

MDS array codes with independent parity symbols

A new family of maximum distance separable (MDS) array codes is presented. The code arrays contain p information columns and r independent parity columns, each column consisting of p-1 bits, where p is a prime. We extend a previously known construction for the case r=2 to three and more parity columns. It is shown that when r=3 such extension is possible for any prime p. For larger values of r, we give necessary and sufficient conditions for our codes to be MDS, and then prove that if p belongs to a certain class of primes these conditions are satisfied up to r ≤ 8. One of the advantages of the new codes is that encoding and decoding may be accomplished using simple cyclic shifts and XOR operations on the columns of the code array. We develop efficient decoding procedures for the case of two- and three-column errors. This again extends the previously known results for the case of a single-column error. Another primary advantage of our codes is related to the problem of efficient information updates. We present upper and lower bounds on the average number of parity bits which have to be updated in an MDS code over GF (2^m), following an update in a single information bit. This average number is of importance in many storage applications which require frequent updates of information. We show that the upper bound obtained from our codes is close to the lower bound and, most importantly, does not depend on the size of the code symbols

X-code: MDS array codes with optimal encoding

We present a new class of MDS (maximum distance separable) array codes of size n×n (n a prime number) called X-code. The X-codes are of minimum column distance 3, namely, they can correct either one column error or two column erasures. The key novelty in X-code is that it has a simple geometrical construction which achieves encoding/update optimal complexity, i.e., a change of any single information bit affects exactly two parity bits. The key idea in our constructions is that all parity symbols are placed in rows rather than columns

Variable Redundancy Coding for Adaptive Error Control

This thesis is concerned with variable redundancy(VR) error control coding. VR coding is proposed as one method of providing efficient adaptive error control for time-varying digital data transmission links. The VR technique involves using a set of short, easy to implement, block codes; rather than the one code of a fixed redundancy system which is usually inefficient, and complex to decode. With a VR system, efficient data-rate low-power codes are used when channel conditions are good, and very high-power inefficient codes are used when the channel is noisy. The decoder decides which code is required to cope with current conditions, and communicates this decision to the encoder by means of a feedback link. This thesis presents a theoretical and practical investigation of the VR technique, and aims to show that when compared with a fixed redundancy system one or more of the advantages of increased average data throughput, decreased maximum probability of erroneous decoding, and decreased complexity can be realised. This is confirmed by the practical results presented in the thesis, which were obtained from field trials of an experimental VR system operating over the HE’ radio channel, and from computer simulations. One consequence of the research has been the inception of a study of codes with disjoint code books and mutual Hamming distance (initially considered for combatting feedback errors), and this topic is introduced in the thesis

Proceedings of the Second International Mobile Satellite Conference (IMSC 1990)

Presented here are the proceedings of the Second International Mobile Satellite Conference (IMSC), held June 17-20, 1990 in Ottawa, Canada. Topics covered include future mobile satellite communications concepts, aeronautical applications, modulation and coding, propagation and experimental systems, mobile terminal equipment, network architecture and control, regulatory and policy considerations, vehicle antennas, and speech compression

The deep space network

The progress is reported of Deep Space Network (DSN) research in the following areas: (1) flight project support, (2) spacecraft/ground communications, (3) station control and operations technology, (4) network control and processing, and (5) deep space stations. A description of the DSN functions and facilities is included