Capacity-approaching non-binary balanced codes using auxiliary data

It is known that, for large user word lengths, the auxiliary data can be used to recover most of the redundancy losses of Knuth’s simple balancing method compared with the optimal redundancy of balanced codes for the binary case. Here, this important result is extended in a number of ways. First, an upper bound for the amount of auxiliary data is derived that is valid for all codeword lengths. This result is primarily of theoretical interest, as it defines the probability distribution of the number of balancing indices that results in optimal redundancy. This result is equally valid for particular non-binary generalizations of Knuth’s balancing method. Second, an asymptotically exact expression for the amount of auxiliary data for the ternary case of a variable length realization of the modified balanced code construction is derived, that, in all respects, is the analogue of the result obtained for the binary case. The derivation is based on a generalization of the binary random walk to the ternary case and a simple modification of an existing generalization of Knuth’s method for the non-binary balanced codes. Finally, a conjecture is proposed regarding the probability distribution of the number of balancing indices for any alphabet size.The National Research Foundation (NRF) and SENTECH Chair in Broadband Wireless Multimedia Communication.http://ieeexplore.ieee.org/servlet/opac?punumber=18hj2019Electrical, Electronic and Computer Engineerin

Quasi-enumerative coding of balanced run-length limited codes

Various methods have been proposed for the construction of balanced run-length limited codes. Amongst these methods is the enumerative coding approach by Kurmaev. The advantage of this approach is that the code has maximum cardinality and thus approaches capacity with increasing codeword length. However, enumerative coding has the disadvantage of becoming prohibitively complex for large codeword lengths. We propose an alternative enumerative coding method that reduces the encoding and decoding complexity. We call it quasi-enumerative coding as it does not follow a strict lexicographic order, but retains a one-to-one mapping between rank and the corresponding balanced run-length limited codeword.https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639hj2024Electrical, Electronic and Computer EngineeringSDG-09: Industry, innovation and infrastructur

A note on non-binary multiple insertion/deletion correcting codes

Abstract: We propose the construction of a non-binary multiple insertion/deletion correcting code based on a binary multiple insertion/deletion correcting code. In essence, it is a generalisation of Tenengol’ts’ non-binary single insertion/deletion correcting code. We evaluate the cardinality of the proposed construction based on the asymptotic upper bound on the cardinality of a maximal binary multiple insertion/deletion correcting code derived by Levenshtein

Moment balancing templates for insertion/deletion correction

M.Ing.In practice, channels with only insertions and deletions are rare. More commonly, additive errors are also present. Therefore, additional redundancy bits are added to the encoded data stream to allow for insertion/deletion correction. In this dissertation, moment balancing templates are used to add a single insertion/deletion capability to an arbitrary additive-error-correcting code. Moment balancing can be used for systematic encoding of number-theoretic codes. The selection of a particular additive-error-correcting codebook has potential influence on the moment balancing template. In direct relation to this, partition distributions of linear sets are considered and their connection to moment balancing templates illustrated. As an alternative to fixed length moment balancing templates, a variable length approach to moment balancing is also considered. It is shown that variable length moment balancing templates result in better performance, in terms of redundancy, than the optimal fixed length moment balancing template. It is assumed that the boundaries of variable length Levenshtein codewords are known. To implement the variable length template in practice, multiple markers are needed. The delimitation of variable length codeword boundaries with these markers leads to longer marker sequences as compared with the fixed length templates

Multiple insertion/deletion correcting and detecting codes : structural analysis, constructions and applications

D.Ing.This thesis is dedicated to an analysis of fundamental topics and issues related to deterministic insertion/deletion correcting and detecting codes. The most important contributions in this respect are the construction of a multiple insertion/deletion correcting code for run-length limited sequences and the construction and applications of multiple deletion (insertion) detecting codes. It is shown how run-length constraints and higher order moments can be combined to create a code which is simultaneously multiple insertion/deletion error correcting and runlength constrained. A systematic form of this code is presented, whereby any arbitrary run-length constrained sequence can be made into a multiple insertion/deletion correcting codeword by adding a prefix. This prefix is appended to the run-length constrained sequence in such a way that the resulting codeword is itself run-length constrained. Furthermore, it is shown that, despite the run-length constraints, the resulting code is guaranteed to have a better asymptotic rate than the Helberg code, the only other known non-trivial deterministic multiple insertion/deletion correcting code. We consider insertion/deletion detecting codes and present a multiple deletion (insertion) detecting code. It is shown that this code, which is systematic, is optimal in the sense that there exists no other systematic multiple deletion (insertion) detecting code with a better rate. Furthermore, we present a number of applications of such codes. In addition, further related topics of interest are considered. Firstly, jitter as a fundamental cause of insertion/deletion errors is investigated and as a result a counterpart to the signal-to-noise ratio in the amplitude domain is proposed for the time domain. Secondly, motivated by the correspondence of Levenshtein and Varshamov-Tenengol’ts codes, we investigate the insertion/deletion correcting capability of the single asymmetric error correcting Constantin-Rao codes within a wider framework of asymmetric error correcting and insertion/deletion correcting code structure correspondences. Finally, we propose a generalisation of Tenengol’ts’ construction for multiple non-binary insertion/deletion correction

Variable- and fixed-length balanced runlength-limited codes based on a Knuth-like balancing method

A novel Knuth-like balancing method for runlength-limited words is presented, which forms the basis of new variable- and fixed-length balanced runlength-limited codes that improve on the code rate as compared to balanced runlength-limited codes based on Knuth's original balancing procedure developed by Immink et al. While Knuth's original balancing procedure, as incorporated by Immink et al., requires the inversion of each bit one at a time, our balancing procedure only inverts the runs as a whole one at a time. The advantage of this approach is that the number of possible inversion points, which needs to be encoded by a redundancy-contributing prefix/suffix, is reduced, thereby allowing a better code rate to be achieved. Furthermore, this balancing method also allows for runlength violating markers which improve, in a number of respects, on the optimal such markers based on Knuth's original balancing method.The National Research Foundation (NRF) and SENTECH Chair in Broadband Wireless Multimedia Communication.http://ieeexplore.ieee.org/servlet/opac?punumber=18hj2020Electrical, Electronic and Computer Engineerin

An analogue to SNR for timing synchronisation motivated by jitter and insertion/deletion errors

Abstract: This paper takes a closer look at the relationship between insertion/deletion errors and one of its most common causes, timing jitter. We consider two insertion/deletion channel models based on different assumptions about the timing jitter. In the literature, only channels with equal insertion/deletion probabilities for each bit have been considered. However, this assumption is only true under certain conditions. A channel, where the probability of insertion/deletion errors increases with time, is another feasible scenario. We derive an approximation for the probability of insertion/deletion errors for both models. With these ideas, we also define a possible counterpart in the time domain to the signal-to-noise ratio (defined in the amplitude domain). As an analogue to Gaussian noise in the amplitude domain, we only consider random Gaussian distributed jitter

Queueing models for cognitive radio networks : a survey

Cognitive radio networks (CRNs) are an emerging paradigm for next generation wireless communication systems allowing for more ef cient radio spectrum utilization. In order to harness the full potential that CRNs may offer, many challenges and problems need to be overcome and addressed. One of the critical questions is the performance of secondary networks under primary user activity constraints. In this respect, queueing assumes a primary role in characterizing the delay, throughput and other performance metrics for secondary users, which in turn has implications for resource allocation, medium access control and quality of service provisioning. This survey presents an overview and classi cation of the various queueing models and techniques which have been proposed in the literature in the context of CRNs. Furthermore, open problems, future research directions and further potential applications related to queueing for CRNs are identi ed.In part by the National Research Foundation (NRF) and in part by the SENTECH Chair in Broadband Wireless Multimedia Communication, University of Pretoria.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639am2018Electrical, Electronic and Computer Engineerin