Joint Source-Channel Coding Using Variable-Length Codes

We address the problem of joint source-channel coding when variable-length codes are used for information transmission over a discrete memoryless channel. Data transmitted over the channel are interpreted as pairs (m _k ,t _k ), where m _k is a message generated by the source and t _k is a time instant when the transmission of the kth codeword begins. The decoder constructs an estimate of the transmitted sequence of pairs, and the kth decoding error is introduced as the event that the pair (m _k ,t _k ) does not belong to this sequence. We describe the maximum likelihood decoding algorithm and prove a lower bound on the exponent of the decoding error probability. For a subclass of discrete memoryless sources and discrete memoryless channels, this bound is asymptotically tight.     

Some bounds on multiparty communication complexity of pointer jumping

We introduce the model of conservative one-way multiparty complexity and prove lower and upper bounds on the complexity of pointer jumping.? The pointer jumping function takes as its input a directed layered graph with a starting node and k layers of n nodes, and a single edge from each node to one node from the next layer. The output is the node reached by following k edges from the starting node. In a conservative protocol, the ith player can see only the node reached by following the first i–1 edges and the edges on the jth layer for each j > i. This is a restriction of the general model where the ith player sees edges of all layers except for the ith one. In a one-way protocol, each player communicates only once in a prescribed order: first Player 1 writes a message on the blackboard, then Player 2, etc., until the last player gives the answer. The cost is the total number of bits written on the blackboard.?Our main results are the following bounds on k-party conservative one-way communication complexity of pointer jumping with k layers:? (1) A lower bound of order for any .?(2) Matching upper and lower bounds of order for . received March 22, 1996     

On the Performance of Permutation Codes for Multi-User Communication

Permutation coding for multi-user communication schemes that originate from the Fast Frequency Hopping/Multiple Frequency Shift Keying modulation is investigated. Each sender is either passive or sends some signal formed as the concatenation of M elementary signals having M different specified frequencies. There is also a jammer, who can introduce disturbances. A single disturbance is either sending the signal that contains all M frequencies at a certain time instant or sending some elementary signal at all time instants. Each receiver receives a vector of M sets, where a set at each time instant contains a fixed frequency if and only if the corresponding elementary signal was sent by either some sender or the jammer. The task of the receiver is to uniquely decode the message of his sender. We present regular constructions of permutation codes for this scheme given the following parameters: the number of frequencies, number of pairs (sender, receiver), number of messages per sender, and maximum number of disturbances of the jammer.     

Constructions of Low-degree and Error-Correcting ε-Biased Generators

In this work we give two new constructions of ε-biased generators. Our first construction significantly extends a result of Mossel et al. (Random Structures and Algorithms 2006, pages 56-81), and our second construction answers an open question of Dodis and Smith (STOC 2005, pages 654-663). In particular we obtain the following results:

Data hiding based on overlapped pixels using hamming code

Most data hiding schemes change the least significant bits to conceal messages in the cover images. Matrix encoding scheme is a well known scheme in this field. The matrix encoding proposed by Crandall can be used in steganographic data hiding methods. Hamming codes are kinds of cover codes. “Hamming + 1” proposed by Zhang et al. is an improved version of matrix encoding steganography. The embedding efficiency of “Hamming + 1” is very high for data hiding, but the embedding rate is low. Our proposed “Hamming + 3” scheme has a slightly reduced embedding efficiency, but improve the embedding rate and image quality. “Hamming + 3” is applied to overlapped blocks, which are composed of 2^k+3 pixels, where k=3. We therefore propose verifying the embedding rate during the embedding and extracting phases. Experimental results show that the reconstructed secret messages are the same as the original secret message, and the proposed scheme exhibits a good embedding rate compared to those of previous schemes.     

An Optimal Algorithm for Broadcasting Multiple Messages in Trees

We consider multiple message broadcasting in tree networks. The source (considered as the root of the tree) has k messages which have to be broadcast to all nodes of the tree. In every time unit each node can send one of its already obtained messages to one of its children. A k-message broadcasting scheme prescribes in which time unit a given node should send a message to which child. It is k-optimal if it achieves the smallest possible time for broadcasting k messages from the source to all nodes. We give an algorithm to construct a k-optimal broadcasting scheme for an arbitrary n-node tree. The time complexity of our algorithm is O(nk), i.e., the best possible.     

Symmetric Rank Codes

As is well known, a finite field _n = GF(q ⁿ ) can be described in terms of n × n matrices A over the field = GF(q) such that their powers A ⁱ , i = 1, 2, ..., q ⁿ – 1, correspond to all nonzero elements of the field. It is proved that, for fields _n of characteristic 2, such a matrix A can be chosen to be symmetric. Several constructions of field-representing symmetric matrices are given. These matrices A ⁱ together with the all-zero matrix can be considered as a _n -linear matrix code in the rank metric with maximum rank distance d = n and maximum possible cardinality q ⁿ . These codes are called symmetric rank codes. In the vector representation, such codes are maximum rank distance (MRD) linear [n, 1, n] codes, which allows one to use known rank-error-correcting algorithms. For symmetric codes, an algorithm of erasure symmetrization is proposed, which considerably reduces the decoding complexity as compared with standard algorithms. It is also shown that a linear [n, k, d = n – k + 1] MRD code _k containing the above-mentioned one-dimensional symmetric code as a subcode has the following property: the corresponding transposed code is also _n -linear. Such codes have an extended capability of correcting symmetric errors and erasures.     

An LSB based novel data hiding method using extended LBP

In this paper we have proposed an LSB based data hiding method. Here, first cover image is encoded by LBP based method (call as ELBP). In ELBP method, a 3 × 3 block is encoded by k bits (1 ≤ k ≤ 9) respect to the central pixel. For data hiding purpose, the cover image is encoded by ELBP then r (1 ≤ r < k) bits are embedded into each neighbor pixel by replacing least r bits of the encoded stream and then modified pixel is processed by OPAP method to improve the quality of the stego image. Proposed method gives high quality stego images with higher embedding rate compare to the state-of-the-art methods. The security of the proposed data hiding method is tested against the attacks like RS steganalysis and Chi-square attack and these methods fail to detect hidden data.

     

The Nonexistence of Ternary [284, 6, 188] Codes

Let [n, k, d] _q codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF(q). Let n _q (k, d) be the smallest value of n for which there exists an [n, k, d] _q code. It is known from [1, 2] that 284 n ₃(6, 188) 285 and 285 n ₃(6, 189) 286. In this paper, the nonexistence of [284, 6, 188]₃ codes is proved, whence we get n ₃(6, 188) = 285 and n ₃(6, 189) = 286.     

An efficient multi-bit steganography algorithm in spatial domain with two-layer security

Steganography is a very useful technique which aims at preventing loss of privacy during the process of data communication, especially over the internet. It can involve different forms of media like image, video (i.e., image sequence), audio etc. We propose a novel steganographic approach in spatial domain using pixel value differencing (PVD) or sample value differencing (SVD) technique and Galois field (GF (2⁸)) operations in order to provide a two layered security for hiding message bits. Our method not only has a very high embedding capacity, but is also capable of withstanding statistical attacks. The proposed method embeds from 2 to 6 bits of the message per pixel in each image component, whereas it can embed a minimum of 6 bits and a maximum of 13 bits of message per sample in audio component at the expense of no perceivable distortion and loss of the cover media quality.

     

Complex polynomials and circuit lower bounds for modular counting

We study the power of constant-depth circuits containing negation gates, unbounded fan-in AND and OR gates, and a small number of MAJORITY gates. It is easy to show that a depth 2 circuit of sizeO(n) (wheren is the number of inputs) containingO(n) MAJORITY gates can determine whether the sum of the input bits is divisible byk, for any fixedk>1, whereas it is known that this requires exponentialsize circuits if we have no MAJORITY gates. Our main result is that a constant-depth circuit of size containingn ^o(1) MAJORITY gates cannot determine if the sum of the input bits is divisible byk; moreover, such a circuit must give the wrong answer on a constant fraction of the inputs. This result was previously known only fork=2. We prove this by obtaining an approximate representation of the behavior of constant-depth circuits by multivariate complex polynomials.     

On Multifold MDS and Perfect Codes That Are Not Splittable into Onefold Codes

The union of disjoint MDS (or perfect) codes with distance 2 (respectively, 3) is always an -fold MDS (perfect) code. The converse is shown to be incorrect. Moreover, if k is a multiple of 4 and n + 1 16 is a power of two, then a k/2-fold k-ary MDS code of length m 3 and an (n + 1)/8-fold perfect code of length n exist from which no MDS (perfect) code can be isolated.     

On the Ranks and Kernels Problem for Perfect Codes

A construction is proposed which, for n large enough, allows one to build perfect binary codes of length n and rank r, with kernel of dimension k, for any admissible pair (r, k) within the limits of known bounds.     

指定验证人的(t,n)门限代理签名方案

将指定验证人概念引入门限代理签名,提出了一个指定验证人的(t,n)门限代理签名方案.该方案不仅实现了门限代理签名,而且还能实现只有指定验证人一起才能验证门限代理签名的特性.在普通的门限代理签名方案中,任何人都能验证门限代理签名的有效性.然而,在某些情况下,只希望指定的验证人一起才能验证门限代理签名.这在实际中是需要的,如电子商务中的电子投标等.另外,该方案还具有在原始签名人需要时,收回某个代理签名人代理权的特性.     

The amount of information and the volume of ‘information tare’

A distinction is suggested between the notions ‘information tare’, the role of which is played by the signals or letters forming the message, and ‘information’, which may be contained in such messages. It is shown that Shannon's definition of the amount of information is, in fact, the definition of the volume of information tare, whereas the amount of information itself may be measured as the volume of information tare of the maximally compact message used for its recording. This allows one to express both the volume of information tare, H, and the amount of information, B, in the same units of measurement–bits–and for any message B≤H. Some consequences of these views are analysed.     

New One-Generator Quasi-cyclic Codes over GF(7)

Let [n,k,d] _q codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF(q). In this paper, seventeen new codes are constructed, which improve the known lower bounds on minimum distance.     

Random Matrices and Codes for the Erasure Channel

The design of erasure correcting codes and their decoding algorithms is now at the point where capacity achieving codes are available with decoding algorithms that have complexity that is linear in the number of information symbols. One aspect of these codes is that the overhead (number of coded symbols beyond the number of information symbols required to achieve decoding completion with high probability) is linear in k. This work considers a new class of random codes which have the following advantages: (i) the overhead is constant (in the range of 5 to 10), independent of the number of data symbols being encoded (ii) the probability of completing decoding for such an overhead is essentially one (iii) the codes are effective for a number of information symbols as low as a few tens (iv) the only probability distribution required is the uniform distribution. The price for these properties is that the decoding complexity is greater, on the order of k ^3/2. However, for the lower values of k where these codes are of particular interest, this increase in complexity might be outweighed by their advantages. The parity check matrices of these codes are chosen at random as windowed matrices, i.e. for each column an initial starting position of a window of length w is chosen and the succeeding w positions are chosen at random as zero or one. It can be shown that it is necessary that w=O(k ^1/2) for the probabilistic matrix rank properties to behave as a non-windowed random matrix. The sufficiency of the condition has so far been established by extensive simulation, although other arguments strongly support this conclusion. The properties of the codes described depend heavily on the rank properties of random matrices over finite fields. Known results on such matrices are briefly reviewed and several conjectures needed in the discussion of the code properties, are stated. The likelihood of the validity of the conjectures is supported through extensive experimentation. Mathematical proof of the conjectures would be of great value for their own interest as well of the particular coding application described here.     

Multireceiver Authentication Codes: Models, Bounds, Constructions, and Extensions

Multireceiver authentication codes allow one sender to construct an authenticated message for a group of receivers such that each receiver can verify authenticity of the received message. In this paper, we give a formal definition of multireceiver authentication codes, derive information theoretic and combinatorial lower bounds on their performance, and give new efficient and flexible constructions for such codes. Finally, we extend the basic model to the case that multiple messages are sent and the case that the sender can be any member of the group.     

Low-randomness constant-round private XOR computations

In this paper we study the randomness complexity needed to distributively perform k XOR computations in a t-private way using constant-round protocols in the case in which the players are honest but curious. We show that the existence of a particular family of subsets allows the recycling of random bits for constant-round private protocols. More precisely, we show that after a 1-round initialization phase during which random bits are distributed among n players, it is possible to perform each of the k XOR computations using two rounds of communication. For , for any c < 1/2, we design a protocol that uses O(kt ²log n) random bits.     

Intuitionistic fuzzy left k-ideals of semirings

We introduce the notion of intuitionistic fuzzy left k-ideals of semirings and investigate their properties and connections with left k-ideals of the corresponding semirings. Next we give some important characterizations of intuitionistic fuzzy left k-ideals of different type and describe various methods of constructions of such intuitionistic fuzzy sets. Finally, we propose some natural classification of intuitionistic fuzzy left k-ideals. The research work was supported by PUCIT.