Luca G. Tallini

Transmission time analysis for the parallel asynchronous communication scheme

In asynchronous systems, the sender encodes a data word with a code word from an unordered code and transmits the code word on the parallel bus lines. In this paper, a transmission time analysis for the above parallel asynchronous communication scheme is presented. It is proven that the average transmission time for a code word is a strictly increasing function of the weight of the code word and it approaches the worst transmission time possible when the weight goes to infinity. This implies that fast parallel asynchronous systems can be designed using low weight codes. This paper also analyzes the transmission time performances of the proximity detecting codes and gives some efficient low constant weight code designs.

Efficient m -ary balanced codes

Abstract An m-ary balanced code with r check digits and k information digits is a code over the alphabet Zm = {0,1, …, m−1} of length n = k+r and cardinality mk such that each codeword is balanced; that is, the real sum of its components (or weight) is equal to [(m − 1)n/2]. This paper contains new efficient methods to design m-ary balanced codes which improve the constructions found in the literature, for all alphabet size m ⩾2. To design such codes, the information words which are close to be balanced are encoded using single maps obtained by a new generalization of Knuths complementation method to the m-ary alphabet that we introduce in this paper. Whereas, the remaining information words are compressed via suitable m-ary uniquely decodable variable length codes and then balanced using the saved space. For any m⩾2, infinite families of m-ary balanced codes are given with r check digits and k⩽[1/(1 − 2α)][mr − 1)/(m − 1)] − c1 (m, α) r −c2(m, α) information digits, where α ϵ [0, 1/2) can be chosen arbitrarily close to 1/2. The codes can be implemented with O(mk logm k) m-ary digit operations and O(m + k) memory elements to store m-ary digits.

On the capacity and codes for the Z-channel

Let p be the 1 to 0 bit error probability and h(p)=-p log/sub 2/ p-(1-p) log/sub 2/ (1-p). The capacity of the Z-channel is given by C/sub Z/=log/sub 2/ (1+(1-p)p/sup p/(1-p)/). For small p, it is shown that C/sub Z//spl ap/1-(1/2)h(p) (vs., C/sub BS/(p)=1-h(p) for the binary symmetric channel). Coding schemes are also given that almost achieve the Z-channel capacity.

Feedback Codes Achieving the Capacity of the Z-Channel

Given the 1 to 0 bit error probability, pisin[0, 1], the capacity of the Z-channel is given by Cz=log2(1+pp/(1-p)-p1/(1-p)). Some new error free feedback coding schemes that achieve the Z-channel capacity are presented.

On efficient high-order spectral-null codes

Let S (N,q) be the set of all words of length N over the bipolar alphabet (-1,+1), having a qth order spectral-null at zero frequency. Any subset of S (N,q) is a spectral-null code of length N and order q. This correspondence gives an equivalent formulation of S(N,q) in terms of codes over the binary alphabet (0,1), shows that S(N,2) is equivalent to a well-known class of single-error correcting and all unidirectional-error detecting (SEC-AUED) codes, derives an explicit expression for the redundancy of S(N,2), and presents new efficient recursive design methods for second-order spectral-null codes which are less redundant than the codes found in the literature.

Revised Gravitational Search Algorithms Based on Evolutionary-Fuzzy Systems

The choice of the best optimization algorithm is a hard issue, and it sometime depends on specific problem. The Gravitational Search Algorithm (GSA) is a search algorithm based on the law of gravity, which states that each particle attracts every other particle with a force called gravitational force. Some revised versions of GSA have been proposed by using intelligent techniques. This work proposes some GSA versions based on fuzzy techniques powered by evolutionary methods, such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE), to improve GSA. The designed algorithms tune a suitable parameter of GSA through a fuzzy controller whose membership functions are optimized by GA, PSO and DE. The results show that Fuzzy Gravitational Search Algorithm (FGSA) optimized by DE is optimal for unimodal functions, whereas FGSA optimized through GA is good for multimodal functions.

On a new class of error control codes and symmetric functions

A general key equation based on elementary symmetric functions is developed for decoding some binary error control codes. Here, the syndrome is obtained by computing the elementary symmetric functions (instead of the power-sums) of the received word. A new class of codes is introduced in this paper which can correct up to t0 0 rarr 1 errors and, simultaneously, up to t1 1 rarr 0 errors. The new key equation can be used to decode this new class of codes and some known codes such as some t-asymmetric error correcting (t-AEC) codes, the t-symmetric error correcting (t-SEC) BCH codes and Goppa codes. Some generalizations to the non binary case are also given.

Systematic t-Unidirectional Error-Detecting Codes over Zm

Some new classes of systematic t-unidirectional error-detecting codes over Zm are designed. It is shown that the constructed codes can detect two errors using two check digits. Furthermore, the constructed codes can detect up to mr-2 + r-2 errors using r ges 3 check bits. A bound on the maximum number of detectable errors using r check digits is also given.

On L 1 -distance error control codes

This paper gives some theory and design of efficient codes capable of controlling (i. e., correcting/detecting/correcting erasure) errors measured under the L<inf>1</inf> distance defined over m-ary words, 2 ≤ m ≤ +∞. We give the combinatorial characterizations of such codes, some general code designs and the efficient decoding algorithms. Then, we give a class of linear and systematic m-ary codes, m = sp with s∈IN and p a prime, which are capable of controlling d ≤ p−1 errors. If n and k∈IN are respectively the length and dimension of a BCH code over GF(p) with minimum Hamming distance d + 1 then the new codes have length n and k′ = k + r log<inf>m</inf> s information digits.

On efficient m-ary balanced codes

An m-ary balanced code is a code of length n over the alphabet Z/sub m/={0,1,..., m-1} such that each codeword is balanced; that is, the real sum of its components (or weight) is equal to [(m-1)n/2]. This paper contains new efficient methods to design m-ary balanced codes which improve the constructions found in the literature, for all alphabet size m/spl ges/2. To design such codes, the information words which are close to be balanced are encoded using single maps defined by a new generalization of Knuths (1986) complementation method to the m-ary alphabet. Whereas, the remaining information words are compressed via some m-ary uniquely decodable variable length codes and then balanced using the saved space.