Visible light communications (VLC) technology is a relatively new emerging telecommunication paradigm. It offers the opportunity to design cost-effective communication systems due to the dual use of the light sources, which are exploited as illumination devices and as communication antennas. However, this technology is mostly deployed in short-range communication applications because of the light diffusion range, which is short by nature. One good response to this dilemma is the implementation of relay-assisted cooperative communication systems. Cooperative VLC systems provide three advantages, which are an increase in the transmission range, an improvement of the detection, hence of the bit error rate (BER), and an improved lighting system. In this paper, we analyze the channel response of a single-relay indoor VLC system based on an amplify-and-forward (AF) strategy. The system takes into account the fact that the relay also receives a reflected message. Results show the influence of the room's reflection index, Lambertian index, the number of scattered rays on the overall channel response and confirms the importance of relay-assisted strategies in improving system's reliability.

The radio frequency spectrum has become very congested and scarce. A response to this dilemma is the implementation of visible light communications (VLC) technology, which is enabled by the dramatic development of light emitting diodes (LEDs) and laser diodes (LDs). VLC has become the most popular emerging telecommunication technology. This is due to the interesting advantages that it provides, which include an unlicensed and large bandwidth, a high throughput capability and a low implementation cost. VLC needs a pivot network in medium and long distance transmissions. The amplify‐and‐forward scenario between the backbone network and VLC is cost‐effective owing to its simplicity when compared to the decode‐and‐forward scenario. MPSK‐CSK is a typical example of cascaded systems in AF scenario with VLC where the backbone channel utilises PSK to convey the message. In this paper, we investigate a forward error correction scheme for cascaded MPSK‐CSK systems. A convolutional encoder is added to the MPSK‐CSK scheme to construct the hybrid trellis coded modulation scheme. Selected 8HTCM systems using set partitioning are investigated and results for a Gaussian channel are presented. Numerical results reveal that 8HTCM achieves up to 2.129 dB of asymptotic coding gain when compared to the corresponding un‐coded MPSK‐CSK system.

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.

One of the restrictions of Visible Light Communications (VLC) technology is related to its transmission range, which is short by nature. This short distance is imposed by the lighting range which barely reaches a couple of hundred meters. This has forced VLC to be applied in specific applications where the transmitting and receiving nodes are close enough to enable communication, in both outdoor and indoor environments. As a result, VLC has not been exploited as access system technology. In this paper, we propose an access communication system using VLC technology. Laser light (LL) sources, reputed for their long lighting range, are exploited for the outdoor access system while in indoor, light emitting diodes (LEDs) are used. The combination of indoor and outdoor is based on an amplify-and-forward (AF) strategy to reduce implementation cost. The overall channel frequency response is presented for varying transmitting parameters such as the outdoor attenuation coefficient, γ, the outdoor transmission distance, L, and the indoor reflection coefficient, ρ.

Spectral shaping codes are digital codes especially designed in such a manner that their alphabets give rise to predetermined frequency spectrum envelopes. This implies that the signal energy of these alphabets will be concentrated into a predetermined range of a given frequency spectrum. The design of digital codes in the above mentioned fashion is done in order to match specific channel constraints in the design of transmission, multiplexing or storage systems. In certain applications it is desirable that spectral shaping codes provide some error correction capability or that they possess an increased robustness to errors. These errors may be introduced during transmission, processing or storage of digital information. In this paper, an interleaving method is introduced to increase the robustness of DC free codes toward burst errors whilst maintaining the spectral shaping property of DC free codes. Interleaving when applied to a coded communication system results in a reduction in the mean bit error rate (BER) of coded bit streams.

With the widespread of light emitting diodes (LEDs) as a primary source of illumination, visible light communication (VLC) offers a lot of potentials by providing both resources and energy saving advantages. This paper presents a practical implementation of an integration of Power Line Communication (PLC) and VLC. The system uses spread frequency shift keying (S-FSK) and on-off keying (OOK) in the PLC and VLC channel respectively. The system is of low complexity, low cost and dedicated to enhance low data rate application of PLC technology. The practical design is compatible with the European Committee for Electrotechnical Standardization (CENELEC) band A and the test are done on a Chinese home environment where the Electric Power Research Institute (EPRI) specifies a 3 kHz to 500 kHz band. Results illustrating the effect of sunlight on this system are presented.

This paper puts in Cascade the power line communications (PLC) channel and the visible light communications (VLC) channel, in order to use the PLC channel as backbone for the VLC channel. This combination is suitable for applications in which hybrid PLC-VLC systems are needed. We investigate the behavior of the cascaded channels for a full link transmission. Quadrature phase shift keying combined with orthogonal frequency division multiplexing (QPSK-OFDM) is used over the PLC channel and color shift keying (CSK) is deployed over the VLC channel to convey the information. Cascaded channel variances are analyzed. Complete simulated bit error rate (BER) is analyzed and presented for multiple scenarii that could occur in the two channels.

Conceptionally the User Datagram Protocol (UDP) should be well-suited for real-time applications, e.g., for Voice over IP (VoIP). However, many such applications, e.g., Skype, use the Transmission Control Protocol (TCP) either as a primary protocol or as a backup protocol when UDP is blocked, despite TCP's flow control-related data delays. This paper proposes a technique for the estimation of the application buffer requirements of such TCP-based applications and the amount of data congestion in real-time TCP data streams. We apply this technique to data collected from a global network exchanging synthetic real-time traffic over TCP. Our results show that the buffering requirements vary widely with time and path but can be substantial in many cases.

Codes are presented that can correct the deletion or the insertion of a predetermined number of adjacent bits greater than or equal to three. This extends the constructions of codes beyond those proposed by Levenshtein fifty years ago to correct one or two adjacent deletions or insertions.

A well-known method for balancing binary sequences, in the sense of forcing them to have as many zeroes as ones, was proposed by Knuth. It is based on the inversion of all bits beyond a certain balancing index, and communicating this index via a prefix. This principle has also been applied to balance runlength-limited (RLL) sequences. Another Knuth-based approach exploits the insertion of a marker in the RLL sequence causing a deliberate runlength violation at the position of the balancing index. This marker method has an advantage over the prefix method, since its redundancy does not grow with the length of the source blocks. In this paper, the markers are optimized with respect to their length and the severeness of the runlength violation, for possible application in future (optical) recording systems.

Permutation codes are advantageous due to their favourable symbol diversity properties and are applied in flash memories combined with rank modulation. Codebooks traditionally consist of permutations with specific distance properties. A class of permutation codes was presented where a codeword consists of a sequence or concatenation of permutations, rather than a single permutation. These codebooks were constructed to correct substitution or deletion errors. In this paper, permutations are concatenated to form codewords with the goal of detecting and correcting adjacent transposition errors. An outer code is used to detect erroneous permutations in the codeword, using additional parity permutations. The symbol diversity of permutation codes is preserved and codebooks with higher cardinalities are constructed which result in better code rates.

A new class of permutation codes is presented where, instead of considering one permutation as a codeword, codewords consist of a sequence of permutations. The advantage of using permutations, i.e. their favourable symbol diversity properties, is preserved. Additionally, using sequences of permutations as codewords, code rates close to the optimum rate can be achieved. Firstly, the complete set of permutations is divided into subsets by using set partitioning. Binary data is then mapped to permutations from these subsets. These permutations, together with a parity permutation, will form the codeword. Two constructions will be presented: one capable of detecting and correcting substitution errors and the other capable of detecting and correcting either substitution or deletion errors.

Insertion/deletion detecting codes were introduced by Konstantinidis In this paper we define insertion/deletion detecting codes in a slightly different manner, and based on this definition, we introduce multiple deletion and multiple insertion detecting codes. It is shown that these codes, which are systematic, are optimal in the sense that there exists no other systematic multiple deletion (insertion) detecting codes with a better rate. One of the limitations of number-theoretic code constructions intended to correct insertion/deletion errors, e.g., the Levenshtein code, is that they require received codeword boundaries to be known in order to successfully decode. In literature, a number of schemes have been proposed to deal with this problem. We show how insertion/deletion detecting codes as presented in this paper can be used to improve and/or extend some of these schemes.

An RDS-minimizing, multi-mode modulation coding scheme, using maximum run-length violating markers and based on the Knuth balancing approach, is applied to run-length limited sequences. Simulations are used to measure spectra and DC suppression performance. A comparison to EFM is included.

For communication schemes employing Frequency Hopping/Multiple Frequency Shift Keying modulation, we present an algorithm for finding good non-binary synchronization sequences, which are permutations, to be used with permutation codes to synchronize/resynchronize data in channels with background noise and interference(frequency jamming/fading). For the synchronization sequences, new analytical expressions for the probability of false acquisition are also given. Using simulation results, we show that our synchronization sequences perform better than some conventional non-binary synchronization sequences, in the presence of background noise and interference.

A proof that the Helberg code is capable of correcting multiple deletion/insertion errors is presented. This code is a generalization of the number-theoretic Levenshtein code which is capable of correcting a single deletion/insertion. However, apart from exhaustive testing of short codes, no proof was hitherto given to verify that the Helberg code is indeed capable of correcting multiple deletions and insertions.

The first-order moment of (d, k)-constrained codes is investigated in this paper. A generalized moment balancing template is proposed to encode a (d, k) sequence into a single insertion or deletion correcting codeword without losing the constraint property. By relocating 0's in moment balancing runs, which appear in a pairwise manner of a (d, k) sequence, the first-order moment of this sequence can be modified to satisfy the Varshamov-Tenengolts construction. With a reasonably large base in the modulo system introduced by the Varshamov-Tenengolts construction, this generalized moment balancing template can be applied to run-length limited sequences. The asymptotic bound of the redundancy introduced by the template for (d, k) sequences is of the same order as the universal template for random sequences and, therefore, the redundancy is small and suitable for long sequences of practical interest.

A code construction is proposed to add a multiple insertion/deletion error correcting capability to a run-length limited sequence. The codewords of this code are themselves run-length limited. The insertion/deletion correcting capability is achieved by requiring several weighted sums of run-lengths in the codewords to satisfy certain congruences modulo primes. The construction is similar to the number-theoretic code proposed by Dolecek and Anantharam, which can correct multiple repetition errors or, equivalently, multiple insertions of zeros. It is shown that if the codewords in this code are run-length limited, then the code is capable of correcting both insertions and deletions of zeros and ones. An algorithm is proposed for decoding over a multiple insertion/deletion channel. Following the work of Dolecek and Anantharam, a systematic encoding method is also proposed for the codes. Furthermore, it is shown that the proposed construction has a higher rate asymptotically than the Helberg code, which is unconstrained in terms of run-lengths, even though our construction has the additional run-length constraints. The need for run-length limited codes that can correct insertion/deletion errors is motivated by bit-patterned media for magnetic recording.

Knuth's celebrated balancing method consists of inverting the first bits in a binary information sequence, such that the resulting sequence has as many ones as zeroes, and communicating the index to the receiver through a short balanced prefix. In the proposed method, Knuth's scheme is extended with error-correcting capabilities, where it is allowed to give unequal protection levels to the prefix and the payload. The proposed scheme is very general in the sense that any error-correcting block code may be used for the protection of the payload. Analyses with respect to redundancy and block and bit error probabilities are performed, showing good results while maintaining the simplicity features of the original scheme. It is shown that the Hamming distance of the code is of minor importance with respect to the error probability.

Knuth published a very simple algorithm for constructing bipolar codewords with equal numbers of +1's and -1's, called balanced codes. In our paper we will present new code constructions that generate balanced runlength limited sequences using a modification of Knuth's algorithm.

The Knuth codeword balancing approach is adapted to a DC-free, RDS-minimizing multi-mode coding scheme. Power spectra and sum variance metrics obtained with simulations are compared with those of the existing Knuth constructions, and error performance is evaluated for a binary symmetric channel.

A new technique of designing spectral null codes with permutation sequences is presented. These new codes have nulls at sub-multiples of the frequency of the transmitted symbols and are also DC-free codes. The choice of the corresponding channel levels given to each transmitted symbols has guaranteed the elimination of the DC component at the lower frequencies and gave an advantage on the binary spectral null codes by being DC-free codes.

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.

The first-order moment of (d, k) constrained codes is investigated in this paper. We propose a generalized moment balancing template to encode a (d, k) sequence into a single insertion or deletion correcting codeword without losing the constraint property. By relocating 0's in moment balancing runs of a (d, k) sequence, the first-order moment of this sequence can be manipulated to satisfy the Varshamov-Tenengolts construction. The moment balancing runs appear in a pairwise manner in this sequence. The lower bound of the number of balancing bits in the template is asymptotically of the same order as the universal template for random sequences, and is of a practical-interest small.

Linear and cyclic codes are typically used to combat substitution errors. However, synchronization errors, associated with the deletion and insertion of symbols, can cause severe performance degradation unless the coding scheme possesses the capability to recover from such errors. It is shown that linear codes of rate greater than 1/2 cannot correct deletion or insertion errors but there are linear codes of rate 1/2 that can correct these errors. Although cyclic codes, except for repetition codes, cannot correct deletion or insertion errors, two approaches are investigated to yield codes, based on cyclic codes, that can correct these errors. In the first approach, it is shown that a binary or nonbinary cyclic code of rate at most 1/3 or 1/2, respectively, can be extended by one symbol to make it capable of correcting synchronization errors. In the second approach, a cyclic code of rate at most 1/2 is expurgated by appropriately deleting codewords such that the expurgated code is capable of correcting synchronization errors. It is shown that deleting codewords costs at most two information bits if the code is binary and one information symbol if the code is nonbinary.

The generalized moment balancing templates for spectral null codes are investigated in this paper. A new approach based on the insertion of a determined number of vectors at determinate indices of a spectral null code word, is found to balance the moment of the code word. Moment balanced code words preserve the spectral null properties and can guarantee the correction of one insertion or one deletion error. As compared to the universal template for an uncoded sequence, the redundancy is determined by the structure of the original spectral null code, however, it can be kept small. The new approach involves the applications of the optimized moment balancing template and nonbinary enumeration of the balancing moment values.

Moment balancing templates have been proposed for channels with a small probability of an insertion/deletion (several orders smaller than additive errors) that add a minimal amount of redundancy. These templates are essentially a systematic way of encoding number-theoretic codes (primarily Levenshtein's s = 1 insertion/deletion code). Moment balancing templates proposed up to this point have been of fixed length. In this paper, it is shown that by using variable length templates, it is possible to obtain better performance than the optimal fixed length moment balancing template. Here, performance is defined as the amount of redundancy, which includes the moment balancing bits and the marker, that needs to be added.

We derive a simple formula to generate a wide-sense systematic generator matrixBfor a Reed-Solomon code. Specifically, we generate the generator matrixBsuch that the columns with indices ¿1, ¿2,..., ¿kare the columns of the identity matrixIk. One possible application of these wide-sense matrices is erasures-only decoding.

Narrowband interference can cause undetected errors when M-FSK data is encoded with an algebraic code containing the all-ecodewords. This is due to the fact that the narrowband interferer will cause the output of the M-FSK demodulator to correspond to one of the all-ecodewords. One possible solution is to use a coset code of a code containing the repetition code. The choice of the coset leader should be such that the resulting coset code has minimum same-symbol weight. We give a general construction for generating coset codes with minimum same-symbol weight and present results where an optimal coset code for an (n, k) Reed-Solomon code is applied in an M-FSK environment with narrowband interference. From the results it is evident that the optimal coset codes outperform linear codes when narrowband interference is present.

A new graph theoretic construction mapping binary sequences to permutation sequences is presented. The k-cube graph construction has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. This contributed in a better way to understand the distance-reducing mapping, which was not investigated before.

Templates are constructed to extend arbitrary additive error correcting or constrained codes, i.e., additional redundant bits are added in selected positions to balance the moment of the codeword. The original codes may have error correcting capabilities or constrained output symbols as predetermined by the usual communication system considerations, which are retained after extending the code. Using some number theoretic constructions in the literature, insertion/deletion correction can then be achieved. If the template is carefully designed, the number of additional redundant bits for the insertion/deletion correction can be kept small-in some cases of the same order as the number of parity bits in a Hamming code of comparable length.

Moment balancing templates have been proposed for channels with a small probability of an insertion/deletion (several orders smaller than additive errors) that add a minimal amount of redundancy. These templates are essentially a systematic way of encoding number-theoretic codes (primarily Levenshteinpsilas s = 1 insertion/deletion code). Moment balancing templates proposed up to this point have been fixed length. In this paper, it is shown, that by using variable length templates, it is possible to obtain better performance than the optimal fixed length moment balancing template. Here, performance is defined as the amount of redundancy that needs to be added.

We investigate moment balancing templates for spectral shaping codes, e.g., dc-free codes, high-order spectral-null codes and spectral nulls code. A new approach by addingkgrouped bits at determinate indices of the code word is found to balance the moment of the code word. Moment balanced code words preserve the spectral-null properties and can guarantee to correct one insertion or deletion error. The redundancy, which is a constant factor greater than that of the universal template for uncoded sequence, can be kept small. The new approach also involves the application of the optimized moment balancing template and the non-binary enumeration of balancing moment values.

A partitioned moment balancing template (systematic encoding of some number theoretic codes) is presented that can correct a single insertion/deletion. Instead of dispersing the moment balancing bits across the template, they are grouped together. Moment balancing templates are used to add insertion/deletion correcting capability to an additive-error-correcting code. The effect of using a particular additive-error-correcting code on the minimum number of moment balancing bits is investigated.

We consider the erasures-only decoding of Reed-Solomon codes. One class of erasure decoders of algebraic codes can be viewed as a transformation of the systematic generator matrix, as first noticed by Berlekamp. We extend Berlekamppsilas method to Reed-Solomon codes and compare the performance of the decoder with various other Reed-Solomon erasure decoders. The developed decoder reduces the decoding time of packet erasures significantly when used in conjunction with a modified interleaver found in the literature.

A new way of looking at permutation distance-preserving mappings (DPMs) is presented by making use of a graph representation. The properties necessary to make such a graph distance-preserving, are also investigated. Further, this new knowledge is used to analyze previous constructions, as well as to construct a new general mapping algorithm for a previous multilevel construction.

The use of linear and cyclic codes for correcting synchronization errors is investigated. These codes are typically required to have the capability to correct substitution errors, which are the most common type of errors in most communication and storage systems. However, synchronization errors, associated with the deletion and insertion of symbols, can also occur and may cause severe performance degradation unless the coding scheme possesses the capability to recover from such errors. We show that linear codes of rate greater than 1/2 cannot correct deletion or insertion errors. Although cyclic codes, except for repetition codes, cannot correct deletion or insertion errors, we show that adding one extra symbol to the codewords of a binary or nonbinary cyclic code of rate at most 1/3 or 1/2, respectively, yields a code capable of correcting a single deletion or insertion.

We investigate extending a chosen block or convolutional code which has additive error correction capability, as predetermined by the usual communication systems or coding considerations. Our extension involves constructing a template to add additional redundant bits in positions, selected to balance the moment of the code word. Using some number theoretic constructions in the literature, insertion/deletion correction can then be achieved. If the template is carefully designed, the number of additional redundant bits for the insertion/deletion correction can be kept small - in some cases of the same order as for Hamming codes. Our construction technique can also be used for the systematic encoding of number theoretic codes, and furthermore have implications for other coding techniques utilizing the moment function, such as codes correcting asymmetrical errors, spectral shaping codes, or constant weight codes.

A multilevel construction is introduced to create distance-preserving mappings from binary sequences to permutation sequences. It is also shown that for certain values, the new mappings attain the upper bound on the sum of Hamming distances obtainable for such mappings, and in the other cases improve on those of previous mappings

A new general upper bound is derived on the sum of the Hamming distances between sequences when mapping from one set of sequences to another. It is shown that a similar upper bound for mappings from binary sequences to permutation sequences is a special case of this upper bound and this is used to evaluate known mappings. Also, new distance-preserving mappings (DPMs) from binary sequences to permutation sequences are presented, based on a multilevel construction. In addition to explicit distance-conserving mappings, distance-increasing, and distance-reducing mappings are also presented. Several of the new DPMs attain the upper bound

We investigate the optimal Hamming distance that is achievable when mapping binary sequences to permutation sequences. This is used to determine how close to optimum some of the known mappings are. Furthermore, using simulation results we show that mappings found by exhaustive search using optimum distance as criterion perform better than previous known mappings

A concatenated system is presented to achieve unequal error protection (UEP) on a channel with insertion/deletion/substitution (IDS) errors. By using a feedback-mapping encoder scheme, the path-pruning of a convolutional code is achieved to periodically generate a specific block code, which can be exploited to correct insertion or deletion errors. This paper presents a general means to obtain a path-pruned convolutional code with specific trellis structure by using the puncturing and pruning processes. One application combining the rate-compatible path-pruned convolutional code, partial interleaving, and Reed-Solomon code was implemented to evaluate its performance on the IDS channel.

We introduce the new concept of permutation trellis codes and present a generalized construction procedure, applying our technique of distance-preserving mappings. Minimum-distance decoding follows naturally, using the Viterbi algorithm. We furthermore investigate the performance of these codes when combined with multitone frequency-shift keying modulation and noncoherent detection in a diversity scheme, to make transmissions robust against narrowband, broadband, and background noise disturbances, such as those encountered in power-line communications.

The Viterbi decoding algorithm provides maximum likelihood decoding and has found widespread application since its introduction in 1967. It is currently the most widely used technique for the decoding of codes having a state system description, including the class of linear error correcting convolutional codes. Contrary to this, it is still common practice to use combinational logic decoders for ternary line codes. These are non-linear codes frequently used in metallic cable systems due to advantages such as efficient utilization of bandwidth, and a DC free power spectral density function. We investigate in this paper the behaviour of Viterbi decoding for the most important ternary line codes, and the coding gain that can be obtained by applying soft-decision decoding. The simplification of the Viterbi decoding implementation and the reduction in latency by shortening its survivor path length, have also been investigated.

It is firstly shown that the use of a fixed length decoding window in a channel that introduces insertions/deletions can propagate the errors to such an extent that stronger insertion/deletion correcting codes must be used. It is further shown that random insertion/deletion correcting codes based on the Levenshtein distance are not optimal for such channels. A modification to the Levensthein distance is proposed and codes based on this distance are shown to be better suited to a channel with a fixed length decoding window. Rates of the codes based on the Levenshtein decoding distance are compared with that of codes based on the Levenshtein distance.

We present a new insertion/deletion detection and correcting decoding scheme for convolutional codes that is based on the Viterbi decoding algorithm. Firstly, we show that, when using a coding scheme that utilises a standard rate, R=k/n, convolutional code and n Viterbi decoders in parallel, it is possible to correct up to n-1 consecutive deletions or insertions. Our results show the effectiveness of this scheme to re-establish bit-synchronisation after the deletion of bits. Further, we investigate the correction of multiple deletions or insertions using standard concatenated coding schemes employing convolutional inner codes, and Reed-Solomon outer codes.

In some networks, data packets either arrive without any bit errors, or one or more packets are lost, with packet switched networks as one of the most evident examples. With real-time data, the delay introduced while recovering from these losses can have a great influence on the quality of service of the application. The paper introduces a decoding algorithm that can recover from bursts of erasures by utilizing cyclic Reed-Solomon codes.

By using a run-length representation of sequences, ways to determine suband supersequences are discussed. This is then used in determining the number of sub- and supersequences of a sequence after double insertions or deletions. It is also used in creating subsequence/supersequence books that are searched to find new double insertion/deletion correcting code books with higher cardinalities than those already known.

We investigate binary, number-theoretic, bit insertion/deletion correcting codes as pioneered by Levenshtein (1965, 1966, 1989). The weight spectra and Hamming distance properties of single insertion/deletion error-correcting codes are analyzed. These relationships are then extended to investigate codes that can correct multiple random insertions and deletions. From these relationships, new bounds are derived and a general construction for multiple insertion/deletion correcting codes is proposed and evaluated.

The maximum number of information bits that can be encoded systematically by the number-theoretic codes of Varshamov and Tenengol'ts (1965) is determined. This number is also studied for the more general class of the group-theoretic Constantin-Rao (1979) codes. Although these codes are at least as large as the Varshamov-Tenengol'ts codes, it is shown that the number of bits that can be systematically encoded using a Constantin-Rao code does not exceed the number of bits that can be systematically encoded using a Varshamov-Tenengol'ts code. In fact, in many cases, the largest Constantin-Rao code has the least number of bits that can be systematically encoded.

We derive an upper bound on the undetected error probability of binary (n, k) block codes used on channels with memory described by Markov distributions. This bound is a generalization of the bound presented by Kasami et al. (1984) for the binary symmetric channel, and is given as an average value of some function of the composition of the state sequence of the channel. It can be extended in particular cases of Markov-type channels. As an example, such an extended bound is given for the Gilbert-Elliott (1960, 1963) channel and Markov channels with deterministic errors determined by the state. We develop a recursive technique for the exact calculation of the undetected error probability of an arbitrary linear block code used on a Markov-type channel. This technique is based on the trellis representation of block codes described by Wolf (1978). Results of some computations are presented.

Presents a generating function for runlength limited sequences intended for binary asymmetrical channels. The channel capacity for such channels is derived from this generating function. The authors furthermore present selected numerical values of channel capacity for these sequences. An expression for the power spectrum of binary maxentropic asymmetrical sequences is given and the influence of the asymmetry on the spectrum is investigated, Two new runlength limited modulation codes which are suitable for use on binary asymmetrical channels are investigated.>

Systematic feedforward trellis codes for 8-PSK and 16-QAM modulation are constructed using a nested step by step algorithm which guarantees a good distance profile. This makes the codes suitable for use with sequential decoding, where a rapidly growing distance profile is needed to reduce the average number of computations. In addition to having a good distance profile, the new codes achieve asymptotic coding gains of up to 6.53 dB. A procedure based upon the Fano (1963) algorithm (FA) is used to calculate the free distance of the new codes. This procedure is very effective for finding the free distances of long trellis codes because of the computational and storage efficiency of the FA. From a comparison of the new systematic feedforward codes with Ungerboeck's (1982, 1987) systematic feedback codes, the authors conjecture that a systematic feedforward code of constraint length 2/spl nu/ can achieve the same free distance as a systematic feedback code of constraint length /spl nu/.>

We investigate the statistical distributions of three events, namely the block error detection, correction and misdetection events of a block code on a discrete renewal inner channel, when this inner channel can be modeled by means of a partitioned Markov chain. In order to represent the above mentioned statistical distributions, we introduce the concept of a "super channel model." Analytical procedures to determine some of the parameters of these super channel models are presented. The application of these models in the design of error control systems, such as ARQ systems, is investigated.>

It is shown that a methodology based on hidden Markov models is applicable to the modeling of slowly varying Rayleigh fading channels with additive Gaussian noise and soft decision outputs. The fading is considered to be frequency nonselective, and ideal demodulation is considered throughout. To prove the validity of robustness of the modeling technique, various results that show good agreement between the simulated channels and the models found are presented. Two soft decision statistical distributions, namely, the soft burst and soft burst interval distributions, are defined and compared. To illustrate the accuracy of the models obtained, the simulation and model outputs are compared for a convolutional encoder with Viterbi decoding and various degrees of interleaving.>

Recursions are developed to determine the error-free runs of error sequences at the output of super channels, which are comprised of some constrained codes employed on renewal inner channels. These error-free runs can be used to obtain the statistical error distribution necessary for evaluating various outer error control codes in concatenated schemes. Experimental evidence that some super channels can be represented with a high degree of numerical precision by partitioned Markov chains is presented.>

A maximum-likelihood algorithm for devising complete decoders for constrained codes and an algorithm for calculating the resulting error multiplication probabilities are presented. These algorithms make it possible to reduce the error multiplication when decoding the symbols of constrained codes or the symbols of various combined error correcting, constrained coding schemes after reception over channels that introduce bit errors into the symbols.>

New combinatorial and algebraic techniques are presented for systematically different (d,k) block codes capable of detecting and correcting single bit-errors, single-peak shift-errors, double adjacent-errors and multiple adjacent erasures. Constructions utilizing channel side information, such as the magnetic recording ternary channel output string, or erasures, do not impose any restriction on The k-constraint, while some of the other constructions require k=2d. Due to the small and fixed number of redundant bits, the rates of both classes of constructions can be made to approach the capacity of the d-constrained channel for long codeword lengths. All the codes can be encoded and decoded with simple, structured logic circuits.>

Seven new systematic convolutional codes with good distance profiles, mostly of rates not previously investigated, have been found. New systematic convolutional codes of rates R=k/n, 4>

The authors present Markov diagrams and tables with the capacities in bits/symbol for input restricted ternary channels with various restrictions on maximum runlengths, digital sum variation, and transitions between extreme signal levels. They derive Gilbert-type lower bounds on the minimum Hamming and Euclidean distances achievable with ternary line codes of rates lower than the capacity of the corresponding input restricted channel. They present some single-symbol-error-correcting ternary line codes, found by computer search methods.>

The transformation of a linear convolutional code into a run-length-constrained or balanced trellis code with the same or larger free distance is investigated. The transformation involves a Hamming-distance-preserving mapping of the set of unconstrained binary symbols of the convolutional code onto a set of suitably constrained symbols. Simple tests to determine if these mappings can exist and a tree search algorithm for finding such mappings are presented.>