This paper introduces a new way of prefix code translation. It helps to finish the whole translation by mapping once (only one comparison instruction is needed for getting the length of prefix code), and returns the o...
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This paper introduces a new way of prefix code translation. It helps to finish the whole translation by mapping once (only one comparison instruction is needed for getting the length of prefix code), and returns the original data and the length of prefix code element. The decoding time is only about four times as many as the time accessing original data directly.
Backscatter communications have been widely applied in wirelessly powered networks. Energy constraint forces the nodes to only backscatter a few bits once, causing backscatter communications unable to be applied in th...
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Backscatter communications have been widely applied in wirelessly powered networks. Energy constraint forces the nodes to only backscatter a few bits once, causing backscatter communications unable to be applied in the applications that require to deliver more data (e.g., an image). It is significant to save energy for backscatter communications so that the nodes can deliver more data with the limited energy. In this letter, the energy-efficient code based backscatter communication (CBBC) is proposed, which makes use of the energy consumption disparity between transmitting/receiving bit 0 and bit 1 in the existing backscatter communications. The energy-efficient prefix codebook is derived from the formulated energy consumption minimization problem. In the CBBC, the codebook is shared by the sender and the receiver of a backscatter link, and the sender breaks the original bit stream into equal-length blocks and delivers the energy-consuming blocks by using their corresponding codewords from which the receiver decodes the original data. The experiments show that the proposed CBBC can save energy for backscatter communication.
In this paper we study some general dynamical properties of the class of one-dimensional permutation cellular automata induced by maximal finite prefix codes defined on the one-sided full shift A(N). Then we define fa...
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In this paper we study some general dynamical properties of the class of one-dimensional permutation cellular automata induced by maximal finite prefix codes defined on the one-sided full shift A(N). Then we define families of codes every member of which induces an onto permutation cellular automaton F, and we investigate some properties of the (topological) dynamical system (A(N), F) such as positive expansiveness, entropy and periodic points. We also define and study a special case of permutation cellular automata, namely, elector automata. which are canonically constructed from codes, and provide classes of cellular automata which attain their limit sets in finite time, and other families without that property. (C) 2006 Elsevier Inc. All rights reserved.
An algorithm for constructing an optimal prefix code of n eqmprobable words over r unequal cost coding letters is given. The discussion is in terms of rooted labeled trees. The algorithm consists of two parts. The fir...
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Non-overlapping codes are a set of codewords such that any nontrivial prefix of each codeword is not a nontrivial suffix of any codeword in the set, including itself. If the lengths of the codewords are variable, it i...
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Non-overlapping codes are a set of codewords such that any nontrivial prefix of each codeword is not a nontrivial suffix of any codeword in the set, including itself. If the lengths of the codewords are variable, it is additionally required that every codeword is not contained in any other codeword as a subword. Let C(n, q) be the maximum size of a fixed-length non-overlapping code of length n over an alphabet of size q. The upper bound on C(n, q) has been well studied. However, the nontrivial upper bound on the maximum size of variable-length non-overlapping codes whose codewords have length at most n remains open. In this paper, by establishing a link between variable-length non-overlapping codes and fixed-length ones, we are able to show that the size of a q-ary variable-length non-overlapping code is upper bounded by C(n, q). Furthermore, we prove that the minimum average codeword length of a q-ary variable-length non-overlapping code with cardinality (C) over tilde, is asymptotically no shorter than n-2 as q approaches infinity, where n is the smallest integer such that C(n-1,q) < (C)over tilde> <= C(n, q)
In this paper, we generalize some properties about prefix codes in [1] , replacing the condition: the language L is finite with the condition: L satisfies \boolean ORxis an element ofeta(L) x(-1) L\ an equivalent desc...
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In this paper, we generalize some properties about prefix codes in [1] , replacing the condition: the language L is finite with the condition: L satisfies \boolean ORxis an element ofeta(L) x(-1) L\ an equivalent description.
It is shown that, if X and Y are prefix codes and Z is a non-empty language satisfying the condition XZ = ZY, then Z is the union of a non-empty family {P-n}(i is an element of I) of pairwise disjoint prefix sets such...
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It is shown that, if X and Y are prefix codes and Z is a non-empty language satisfying the condition XZ = ZY, then Z is the union of a non-empty family {P-n}(i is an element of I) of pairwise disjoint prefix sets such that XPi = PiY for all i is an element of 1. Consequently, the conjugacy relations of prefix codes are explored and, under the restriction that both of X and Y are prefix codes, the solutions of the conjugacy equation XZ = ZY for languages are determined. Also, the decidability of the conjugacy problem for finite prefix codes is confirmed. (C) 2016 Elsevier B.V. All rights reserved.
We investigate the ratio ma of prefix codes to all uniquely decodable codes over an n-letter alphabet and with length distribution L. For any integers n >= 2 and m >= 1, we construct a lower bound and an upper b...
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We investigate the ratio ma of prefix codes to all uniquely decodable codes over an n-letter alphabet and with length distribution L. For any integers n >= 2 and m >= 1, we construct a lower bound and an upper bound for inf(L rho n,L), the infimum taken over all sequences L of length m for which the set of uniquely decodable codes with length distribution L is nonempty. As a result, we obtain that this infimum is always greater than zero. Moreover, for every m >= 1 it tends to I when n -> infinity, and for every n >= 2 it tends to 0 when m -> infinity. In the case m = 2, we also obtain the exact value for this infimum. (C) 2018 Elsevier B.V. All rights reserved.
Minimum redundancy coding (also known as Huffman coding) is one of the enduring techniques of data compression. Many efforts have been made to improve the efficiency of minimum redundancy coding, the majority based on...
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Minimum redundancy coding (also known as Huffman coding) is one of the enduring techniques of data compression. Many efforts have been made to improve the efficiency of minimum redundancy coding, the majority based on the use of improved representations for explicit Huffman trees. In this paper, we examine how minimum redundancy coding can be implemented efficiently by divorcing coding from a code tree, with emphasis on the situation when n is large, perhaps on the order of 10(6). We review techniques for devising minimum redundancy codes, and consider in detail how encoding and decoding should be accomplished. In particular, we describe a modified decoding method that allows improved decoding speed, requiring just a few machine operations per output symbol (rather than for each decoded bit), and uses just a few hundred bytes of memory above and beyond the space required to store an enumeration of the source alphabet.
Let A* be a free monoid generated by a finite alphabet A and let A(+) = A*\ {1}, where 1 is the empty word. Let M = {L\L subset of or equal to A(+) or L = {1}} be the monoid of languages under the catenation. We consi...
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Let A* be a free monoid generated by a finite alphabet A and let A(+) = A*\ prefix code, where 1 is the empty word. Let M = {L\L subset of or equal to A(+) or L = prefix code} be the monoid of languages under the catenation. We consider prefix code as a prefix code. The family of all prefix codes p is a free submonoid of M. For any L is an element of M, let L-L = {L' is an element of M\LL' is an element of P}. We show that L-L boolean OR prefix code is a submonoid of p for every non-empty language L subset of or equal to A(+). The purpose of this note is to give a characterization for a finite language L in which L-L boolean OR prefix codeis a free submonoid of P for the case \A\ greater than or equal to 2. For an infinite language L whether the monoid L-L boolean OR prefix code is free or not depends on L. We illustrate the above two cases with examples.
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