In this paper we address the class of anti-uniform Huffman (AUH) codes, also named unary codes, for sources with finite and infinite alphabet, respectively. Geometric, quasi-geometric, Fibonacci and exponential distributions lead to anti-uniform sources for some ranges of their parameters. Huffman coding of these sources results in AUH codes. We prove that, in general, sources with memory are obtained as result of this encoding. For these sources we attach the graph and determine the transition matrix between states, the state probabilities and the entropy. We also compute the average cost for these AUH codes.

In this paper we consider the class of anti-uniform Huffman (AUH) codes for sources with infinite alphabet.Poisson, negative binomial, geometric and exponential distributions lead to infinite anti -uniform sources for some ranges of their parameters.Huffman coding of these sources results in AUH codes.We prove that as a result of this encoding, we obtain sources with memory.For these sources we attach the graph and derive the transition matrix between states, the state probabilities and the entropy.If c 0 and c 1 denote the costs for storing or transmission of symbols "0" and "1", respectively, we compute the average cost for these AUH codes.

In this paper we consider the class of generalized anti-uniform Huffman (AUH) codes for sources with infinite alphabet and geometric distribution. This distribution leads to infinite anti - uniform sources for some ranges of its parameters. Huffman coding of these sources results in AUH codes. We perform a generalization of binary Huffman encoding, using a M-letter code alphabet and prove that as a result of this encoding, sources with memory are obtained. For these sources we attach the graph and derive the transition probabilities between states, as well as the state probabilities. The entropy and the average cost for AUH codes are derived.

This paper shows a link between the dispersion and the nonlinearity degree of QPP (quadratic permutation polynomial) interleavers. An upper bound for the dispersion of QPP interleavers is derived. This upper bound is computed very simple, only depending on the coefficient of x(2) of the polynomial and of the length of interleaver. The comparison with the real dispersion of QPP interleavers given by Takeshita in [1] leads to insignificant difference. Searching of QPP interleavers based on a metric including upper bound of dispersion and D parameter is equivalent with that based on Omega metric.

The paper proposes a general method to analyze discrete sources with memory. Besides the classical entropy, we define new information measures for discrete sources with memory, similar to the information quantities specific to discrete channels. On the base of this method, we show for the first time that, as result of convolutional and turbo encoding, sources with memory are obtained. We apply this information analysis method for the general case of a recursive convolutional encoder of rate RCC=1/n0 and memory of order m, and for a turbo encoder of rate RTC=1/3, with two systematic recursive convolutional component encoders. Each component encoder has memory of order m, and is built based on the same primitive feedback polynomial. For the convolutional and turbo codes, the information quantities H(Y/S), H(S,Y), H(S/Y), H(Y), H(S) and I(S,Y) have been computed, where S and Y denote the set of states and the set of messages of the encoder, respectively. The analysis considered two cases: n0≤m+1 and n0>m+1. When n0=m+1, the mutual information I(S,Y) is maximum and equal to m, as is the entropy of the set of states. For turbo codes, the quantity I(S,Y) also depends on the input bit and on its probability.

In this paper we consider the class of anti-uniform Huffman (AUH) codes for sources with infinite alphabet generated by Poisson distribution. Huffman encoding of these sources results in AUH codes. As a result of this encoding, we obtain sources with memory. The entropy and average cost of these sources with memory are derived. We perform an analogy between sources with memory and discrete memoryless channels, showing that the entropy of the source with memory is similar to the mean error of the discrete memoryless channel. The information quantity I(X,S) specifies for AUH codes whether they are with memory or not, as it differs from zero or is equal to zero, respectively.

Considering the input data generated by a binary Markov source X, linear, binary, block codes are characterized as cyclic sources with memory. The encoding graph for systematic linear block codes is determined. It is shown the encoded data are the output of a binary, cyclic source with memory. The states of this source Y are organized in n classes of states, where n is the length of the code words. The matrix PY of transition probabilities between states is derived, as well as the matrix πy containing the states probabilities. Finally, the entropy H(Y) is computed and a relationship between H(Y) and H(X) is derived.

This paper proposes and proves a theorem which stipulates sufficient conditions the coefficients of two quadratic permutation polynomials (QPP) must satisfy, so that the permutations generated by them are identical. The result is used to reduce the search time of QPP interleavers with lengths given by Long Term Evolution (LTE) standard up to 512, by improving the distance spectrum over the set of polynomials with the largest spreading factor. Polynomials that lead to better performance compared to LTE standard are found for several lengths. Simulations show that 0.5 dB coding gains can be obtained compared to LTE standard.

Considering the input data generated by a binary Markov source X, linear, binary, block codes are characterized as cyclic sources with memory. The encoding graph for systematic linear block codes is determined. It is shown the encoded data are the output of a binary, cyclic source with memory. The states of this source Y are organized in n classes of states, where n is the length of the code words. The matrix PY of transition probabilities between states is derived, as well as the matrix πy containing the states probabilities. Finally, the entropy H(Y) is computed and a relationship between H(Y) and H(X) is derived.

The linear, binary, block codes with no equally likely probabilities for the binary symbols are analyzed.The encoding graph for systematic linear block codes is proposed.These codes are seen as sources with memory and the information quantities H(S,X), H(S), H(X), H(X|S), H(S|X), I(S,X) are derived.On the base of these quantities, the code performances are analyzed.

Two search methods of quadratic permutation polynomials (QPP) for interleavers used in turbo codes are proposed. These methods lead to larger minimum distances and smaller multiplicities compared to interleavers proposed by Takeshita in [1]. The search is accomplished in a limited set of polynomials, that is, those for which the spreading factor and Ω′ metric are maximum. The minimum distance is computed by means of Garello algorithm in which the maximum weight of information sequence is 3 or 4, reducing the search time. The results obtained for various lengths show the efficiency of the proposed methods.

This paper presents new results of the D-ary Huffman tree. These results are used to prove that the maximum value of the average codeword length is obtained for the uniform distribution. The upper bound computed in this paper is higher than the value obtained for Huffman codes with minimum redundancy.

In this paper an information analysis for lossless compression of a large class of discrete sources is performed. The lossless compression is performed by means of a Huffman code with an alphabet A of size M. Matrix characterization of the encoding as a source with memory is realized. The information quantities H(S,A), H(S), H(A), H(A|S), H(S|A), I(S,A) as well as the minimum average code word length are derived. Three extreme cases, p = M-1, p = 0 and M = 2, p = 1 have been analyzed.

This paper presents the lower bound on the average codeword length of the D-ary Huffman codes. Two extreme cases are analyzed: the quasi-uniform and anti-uniform Huffman codes. For each case the codeword lengths are computed. The histogram of the average codeword length obtained by simulation confirms the bound on the average codeword lengths. The lower bound computed in this paper is lower than the value obtained for Huffman codes with minimum redundancy.

In this paper M-ary antiuniform Huffman codes are considered. In this case the source probability distribution assures the minimum average codeword length, by diversifying only one node on each level in the tree graph. A matrix characterization of the M-ary antiuniform Huffman code as a source with memory is performed and the information quantities are derived.

We analyze the lossless compression for a large class of discrete complete and memoryless sources performed by a generalized Huffman with an alphabet consisting of M letters. Given the number of source messages, N, the alphabet size, M, and the number of code words, p, on each level in the graph, excepting the last two ones, we have determined the unknown encoding parameters, that is, the number n of the levels in the encoding graph, the number q of code words on the level n-1, the number k of groups of M nodes, and the remaining m nodes on the last level. The average code word length is also computed. Two extreme cases, when p=0 and p=M-1 have been analyzed.

Two search methods of quadratic permutation polynomials (QPP) for interleavers used in turbo codes are proposed. These methods lead to larger minimum distances and smaller multiplicities compared to the interleavers proposed by Takeshita in (Takeshita 1 ). The search is accomplished in a limited set of polynomials, that is, those for which the spreading factor and Ω′ metric are maximum. The minimum distance is computed by means of Garello algorithm in which the maximum weight of information sequence is 3 or 4, reducing the search time. The results obtained for two particular component codes show the efficiency of the proposed methods.

This paper develops a framework for the synthesis of a feedforward controller for both discrete and continuous linear time variant (LTV) systems. The proposed method determines the structure of a feedforward controller, which is cascaded with the known time varying process, so that the ensemble behaves as a linear time invariant (LTI) system, satisfying certain design requirements. The obtained controller is simple, consisting in a parallel bank of first or second order LTI filters, followed by amplifiers with time variable gain. Simulation results are included to illustrate theoretical considerations. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

A method to increase the minimum distance for turbo codes with Welch-Costas interleavers is proposed. The minimum distance obtained by the proposed method is comparable to that corresponding to the S-random interleaver [1]. A slight increase of memory is required compared to the classic Welch-Costas interleaver [2].