A compound error is any combination of burst errors with various burst lengths including random errors. The compound weight of any such error is defined as a kind of combinational metric which is a generalization of Gabidulin's metric. First, we present a fast method for calculating the weight of any word. Based on this method, as an extension of Wadayama's augmenting method in the case of Hamming weight, we propose a method of constructing codes having higher coding rate by augmenting any compound-error-correcting codes. Furthermore, we show some examples of good compound-error-correcting codes obtained by using our augmenting method.

We investigated the truncated convolutional code with the characteristics of a block code for block-based communication systems. Three truncation methods (direct truncation, tail-terminating, and tail-biting method) were introduced by other researchers. Each of the three methods has a weakness: the direct truncation method decreases the minimum distance, the tail-terminating method uses tail bits, and the tail-biting method can only be applied by using a complicated decoder. Although the tail-biting method gives a better BER performance than the other two methods, we cannot apply the tail-biting method in all situations. Occasionally, the tail-biting convolutional code does not exist. Wang et al. presented two necessary conditions for the existence of the tail-biting convolutional code of the rate-1/2 recursive systematic convolutional code. In this paper, we analyze the encoder of the convolutional code as a linear time invariant system, and present two theorems and six corollaries on the existence of the tail-biting convolutional code. These existence conditions are adaptable to all convolutional codes. In the communication system using the truncated convolutional code, these results are applicable to determining the truncation method.

In this letter, we introduce a two-state turbo-TCM scheme based on the concatenated tree codes. The proposed scheme can achieve near capacity performance yet has considerably lower decoding complexity compared with other existing turbo-TCM codes.

Near-optimality of subcodes of the cyclic Hamming codes is demonstrated on the binary additive channel whose noise process is the two-state homogeneous Markov chain, which is a model of bursty communication channels.

Recently, Vatan, Roychowdhury and Anantram have presented two types of revised versions of the Calderbank-Shor-Steane code construction, and have also provided an exhaustive procedure for determining bases of quantum error-correcting codes. In this paper, we investigate the revised versions given by Vatan et al., and point out that there is no essential difference between them. In addition, we propose an efficient algorithm for searching for bases of quantum error-correcting codes. The proposed algorithm is based on some fundamental properties of classical linear codes, and has much lower complexity than Vatan et al.'s procedure.

A sufficient condition for a code to be optimum on discrete channels with finite input and output alphabets is given, where being optimum means achieving the minimum decoding error probability. This condition is derived by generalizing the ideas of binary perfect and quasi-perfect codes, which are known to be optimum on the binary symmetric channel. An application of the sufficient condition shows that the code presented by Hamada and Fujiwara (1997) is optimum on the q-ary channel model proposed by Fuja and Heegard (1990), where q is a prime power with some restriction. The channel model is subject to two types of additive errors of (in general) different probabilities.

Motivated by intention to evaluate asymptotically multiple-burst-error-correcting codes on channels with memory, we will derive the following fact. Let {Zi } be a hidden Markov process, i. e. , a functional of a Markov chain with a finite state space, and Wb(Z1Z2Zn) denote the number of burst errors that appear in Z1Z2Zn, where the number of burst errors is counted using Gabidulin's burst metric , 1971. As the main result, we will prove the almost sure convergence of relative burst weight Wb(Z1Z2Zn)/n, i. e. , the relative frequency of occurrence of burst errors, for a broad class of functionals { Zi } of finite Markov chains. Functionals of Markov chains are often adopted as models of the noises on channels, especially on burst-noise channels, the most famous model of which is probably the Gilbert channel proposed in 1960. Those channel models described with Markov chains are called channels with memory (including channels with zero-memory, i. e. , memoryless ones). This work's achievement enables us to extend Gilbert's code performance evaluation in 1952, a landmark that offered the well-known Gilbert bound, discussed its relationship to the (memoryless) binary symmetric channel, and has been serving as a guide for the-Hamming-metric-based design of error-correcting codes, to the case of the-burst-metric-based codes (burst-error-correcting codes) and discrete channels with or without memory.

We proposed a soft-decision decoding algorithm for cyclic codes based on energy minimization principle. This letter presents the algorithm which improves decoding performance and decoding complexity of the previous method by giving more initial positions and introducing a new criterion for terminating the decoding procedure. Computer simulation results show that both the decoded block error rate and the decoding complexity decrease by this method more than by the previous method.

We derive an upper bound on the size of a block code with prescribed burst-error-correcting capability combining those two ideas underlying the generalized Singleton and sphere-packing bounds. The two ideas are puncturing and sphere-packing. We use the burst metric defined by Gabidulin, which is suitable for burst error correction and detection. It is demonstrated that the proposed bound improves previously known ones for finite code-length, when minimum distance is greater than 3, as well as in the asymptotic forms.

We propose a novel soft-decision decoding algorithm for cyclic codes based on energy minimization principle. The well-known soft-decision decoding algorithms for block codes perform algebraic (hard-decision) decoding several times in order to generate candidate codewords using the reliability of received symbols. In contrast, the proposed method defines energy as the Euclidean distance between the received signal and a codeword and alters the values of information symbols so as to decrease the energy in order to seek the codeword of minimum energy, which is the most likely codeword. We let initial positions be the information parts of signals obtained by cyclically shifting a received signal and look for the point, which represents a codeword, of minimum energy by moving each point from several initial positions. This paper presents and investigates reducing complexity of the soft-decision decoding algorithm. We rank initial positions in order of reliability and reduce the number of initial positions in decoding. Computer simulation results show that this method reduces decoding complexity.

In this paper a new class of single error-correcting fixed block-length (d, k) codes has been proposed. The correctable error types are peak-shift error, insertion or deletion error, symmetric error, etc. The basic technique to construct codes is a systematic construction algorithm of multilevel sequences with a constant Lee weight (TALG algorithm). The coding rate and efficiency are considerably good, and hence the proposed new codes will be very useful for improving the reliability of high density magnetic recording.

In this paper we propose a class of byte-error-correcting codes derived from algebraic curves which is a generalization on the Reed-Solomon codes, and present their fast parallel decoding algorithm. Our algorithm can correct up to (m + b -θ)/2b byte-errors for the byte length b, where m + b -θ + 1dG for the Goppa designed distance dG. This decoding algorithm can be parallelized. In this algorithm, for our code over the finite field GF (q), the total complexity for finding byte-error locations is O (bt(t + q - 1)) with time complexity O (t(t + q - 1)) and space complexity O(b), and the total complexity for finding error values is O (bt(b + q - 1)) with time complexity O (b(b + q - 1)) and space complexity O (t), where t(m + b -θ)/2b. Our byte-error-correcting algorithm is superior to the conventional fast decoding algorithm for randomerrors in regard to the number of correcting byte-errors in several cases.

Motivated by the design of fault-tolerant multiprocessor interconnection networks, this paper considers the following problem: Given a positive integer t and a graph H, construct a graph G from H by adding a minimum number Δ(t, H) of edges such that even after deleting any t edges from G the remaining graph contains H as a subgraph. We estimate Δ(t, H) for the hypercube and torus, which are well-known as important interconnection networks for multiprocessor systems. If we denote the hypercube and the square torus on N vertices by QN and DN respectively, we show, among others, that Δ(t, QN) = O(tN log(log N/t + log 2e)) for any t and N (t 2), and Δ(1, DN) = N/2 for N even.

The aliasing probability was analyzed for MISRs when the error probability for each input was different. A closed form expression was derived by applying the complete weight distributions of linear codes over a Galois field and its dual codes. The aliasing probability for MISRs characterized by non-primitive polynomials was also analyzed. The inner product for binary representation of symbols was used instead of multiplication over a Galois field. The results show the perfect expression for analyzing the aliasing probability of MISRs.

This paper describes an error-correcting parser (ec-parser) for context-free languages that is an extension of the Leiss's parser. Since the ec-parser uses precomputed informations and a pruning technique by lookahead, the ec-parser is always faster than the Lyon's parser. Several examples are shown.

A soft-decision decoding algorithm for binary linear block codes is proposed. This algorithm seeks to minimize the block error probability. With careful examinations of the first hard-decision decoded results, the candidate codewords are efficiently searched for. Thus, we can reduce the decoding complexity (the number of hard-decision decodings) and lower the block error probability. Computer simulation results are presented for the (23, 12) Golay code. They show that the decoding complexity is considerably reduced and the block error probability is close to that of the maximum likelihood decoder.

As RAMs become dense, their reliability reduces because of complex interactions between memory cells and soft errors due to alpha particle radiations. In order to rectify this problem, RAM manufacturers have started incorporating on-chip (built-in) ECC. In order to minimize the area overhead of on-chip ECC, the same technology is used for implementing the check bits and the information bits. Thus the check bits are exposed to the same failure modes as the information bits. Furthermore, faults in the check bits will manifest as uncorrectable multiple errors when a soft error occurs. Therefore it is important to test the check bits for all failure modes expected of other cells. In this paper, we formulate the problem of testing RAMs with on-chip ECC capability. We than derive necessary and sufficient conditions for testing the check bits for arbitrary and adjacent neighborhood pattern sensitive faults. We also provide an efficient solution to test a memory array of N bits (including check bits) for 5-cell neighborhood pattern sensitive faults in O (N) reads and writes, with the check bits also tested for the same fault classes as the information bits.

This paper investigates a multihopping scheme for MFSK (Multilevel Frequency Shift Keying) /FH-SSMA (Frequency Hopping-Spread Spectrum Multiple Access) system. Moreover, we propose and investigate a modified decoding scheme for the coded MFSK/FH-SSMA system. In this multi-hopped MFSK/FH-SSMA system, several hopping frequencies per chip are assigned and transmitted in parallel in order to improve its frequency diversity capability for a fading channel. We theoretically analyze the performance of the multihopped MFSK/FH-SSMA system in a Rayleigh fading channel. Moreover, in the coded MFSK/FH-SSMA system, we propose a modified scheme of the error and erasure decoding of an error-correcting code. The modified decoding scheme utilizes the information of rows having the largest number of entries in the decoded time-frequency matrix. Their BER (Bit Error Rate) performance is evaluated by theoretical analysis in order to show the improvement in user capacity.

Although individual segments of a natural language such as words have different importance on human interpretation of the meaning, every segment has been uniformly protected by an error-correcting code. If the importance of individual segments is defined by considering their meaning in the sentence, we can adaptively control the level of error-protection for each segment according to its importance in order to reduce errors on human interpretation of the meaning. In this paper, we propose an error-control scheme based on the varying importance of each word. We first introduce a method which determines the importance of each word and then propose an error-control scheme in which several error-correcting codes are alternately used to protect each word according to its importance. Probablity of semantic errors, that is, errors on human interpretation of the meaning, is defined and used as a criterion in mapping error-correcting codes to words possessing different importance. We theoretically formalize the problem of obtaining an optimum mapping which minimizes the probability of semantic errors under some constraint. Given a certain probability distribution of the importance of words and set of error-correcting codes, we can derive the optimum mapping. The proposed error-controlling scheme is theoretically evaluated by comparing its probability of semantic errors with that of a conventional scheme in which every word is uniformly protected by a single error-correcting code. Results show that the proposed scheme can considerably raduce the probability of semantic errors while retaining the same average transmission rate or redundancy.

In this letter, we consider a magnetic or optical recording system employing a concatenated code that consists of a runlength-limited (d, k) block code as an inner code and a byte-error-correcting code as an outer code. (d, k) means that any two consecutive ones in the code bit stream are separated by at least d zeros and by at most k zeros. The minimum separation d and the maximum separation k are imposed in order to reduce intersymbol interference and extract clock control from the received bit stream, respectively. This letter recommends to use as the outer code a unidirectional-byte-error-correcting code instead of an ordinary byte-error-correcting code. If we devise the mapping of the code symbols of the outer code onto the codewords of the inner code, we may improve the error performance. Examples of the mappings are described.