A semidefinite program for distillable entanglement

We show that the maximum fidelity obtained by a positive partial transpose (p.p.t.) distillation protocol is given by the solution to a certain semidefinite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillable entanglement). In the presence of symmetry, the semidefinite program simplifies considerably, becoming a linear program in the case of isotropic and Werner states. Using these techniques, we determine the p.p.t. distillable entanglement of asymmetric Werner states and “maximally correlated” states. We conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1-local distillation     

New upper bounds on the size of codes correcting asymmetric errors (Corresp.)

New upper bounds on the size of codes correcting asymmetric errors are derived by sharpening some of the constraints in the integer programming problem of Delsarte and Piret. It is shown that their code for length9and asymmetric distance2is optimal.     

On the optimal power-distortion tradeoff in asymmetric gaussian sensor network

We present necessary and sufficient conditions, similar to the recent results of Gastpar [1], for the achievability of all power-distortion tuples (P,D) = (P_{1, P2, · · · , PL,D) in an asymmetric Gaussian sensor network where L distributed sensors transmit noisy observations of a Gaussian source through a Gaussian multiple access channel to a fusion center. We show numerically that in general the gap between the provided upper bound and the lower bound of the distortion D is small. We also provide an optimal power allocation that minimizes the total power consumption, P = L i=1 Pi, for uncoded transmission scheme while satisfying a given distortion constraint D. Numerical evaluations show that by applying the optimal power allocation uncoded transmission can perform nearly optimal in an asymmetric sensor network subject to a sum-power constraint. In the symmetric case both bounds agree and provide the optimal power-distortion tradeoff (P,D); this agrees with result of [1]. Thus, in the sense of achieving the optimal (P,D) tradeoff, uncoded transmission is optimal in the symmetric case and can be nearly-optimal in the asymmetric case.}     

Combinatorial analysis of the minimum distance of turbo codes

In this paper, new upper bounds on the maximum attainable minimum Hamming distance of turbo codes with arbitrary-including the best-interleavers are established using a combinatorial approach. These upper bounds depend on the interleaver length, the code rate, and the scramblers employed in the encoder. Examples of the new bounds for particular turbo codes are given and discussed. The new bounds are tighter than all existing ones and prove that the minimum Hamming distance of turbo codes cannot asymptotically grow at a rate more than the third root of the codeword length     

广义Hamming重量上,下界的对偶定理

本文给出了一种广义Ｈａｍｍｉｎｇ重量上、下界的对偶定理。即若给定一个码的对偶码的广义Ｈａｍｍｉｎｇ重量上界（或者下界），可以给出该码的广义Ｈａｍｍｉｎｇ重量上界（或者下界）。Ｈ．Ｓｔｉｃｈ－ｎｏｔｈ（１９９４）曾给出了迹码（如ＢＣＨ码和Ｇｏｐｐａ码的对偶码）的广义Ｈａｍｍｉｎｇ重量一种上、下界，如果采用本文结果就可以给出迹码的对偶码的广义Ｈａｍｍｉｎｇ重量一种上、下界。因此，本文的结果是Ｈ．Ｓｔｉｃｈｎｏｔｈ的结果的有益补充     

Some new upper bounds on the covering radius of binary linear codes

A Griesmer-like upper bound on the covering radius, R, is given. To the author's knowledge this is the only upper bound which explicitly depends on all three parameters n, k, and d. An upper bound on R for cyclic codes is then given which depends on the generator polynomial of the cyclic code and which, in many cases, leads to an improvement of the previous bound. An upper bound on the irreducible generator polynomial cyclic codes is also given. New interpretations and applications of the so-called Norse bounds and necessary and sufficient conditions to attain one of these bounds are provided. Generalizations of most of the results for codes over GF(q) are outlined     

Reliability function of a discrete memoryless channel at rates above capacity (Corresp.)

Asymptotically coincident upper and lower bounds on the exponent of the largest possible probability of the correct decoding of block codes are given for all rates above capacity. The lower bound sharpens Omura's bound. The upper bound is proved by a new and simple combinatorial argument.     

On upper bounds for unrestricted binary-error-correcting codes

In this paper improved upper bounds are obtained forA(n,d), the maximum number of binary code vectors in a code of block lengthnand minimum distanced. Known bounds are presented in a unified way and then refined, giving improvement over best previously published results in almost all cases. Finally, tabulations of the improved results are given. Asymptotically, the new bounds agree with those given by Elias.     

A logarithmic upper bound on the minimum distance of turbo codes

We derive new upper bounds on the minimum distance, which turbo codes can maximally attain with the optimum interleaver of a given length. The new bounds grow approximately logarithmically with the interleaver length, and they are tighter than all previously derived bounds for medium-length and long interleavers. An extensive discussion highlights the impacts of the new bounds in the context of interleaver design and provides some new design guidelines.     

Bounds for Queue Lengths in a Contention Packet Broadcast System

A finite number of users communicating through a broadcast channel is considered. Each user has a buffer of infinite capacity, and a user randomly accesses the channel (ALOHA-type protocol). Moreover, only one packet per user might be sent in an access time. Both symmetric and asymmetric models are considered; that is, we assume either indistinguishable or distinguishable users. An exact analysis of the queue lengths in that type of system is not now available, and therefore, based on some algebraic studies, we shall present some lower and some upper bounds for the average queue lengths. These bounds are quite tight for a small number of users and acceptable for a wide range of input parameters in the symmetric case. In the asymmetric case the bounds are acceptable only for light input traffic and a small number of users.     

Tight bounds on the redundancy of Huffman codes

A method for deriving optimal upper bounds on the redundancy of binary Huffman codes in terms of the probability p₁ of the most likely source letter is presented. This method will be used to compute bounds for all p₁⩾1/127, which were previously known only for a few special cases. Furthermore, the known optimal lower bound for binary Huffman codes is generalized to arbitrary code alphabets and some upper bounds for D-ary Huffman codes, 2⩽D<∞, are given, which are the tightest possible for all p₁⩾1/2     

Upper Bounds on the Rate of LDPC Codes for a Class of Finite-State Markov Channels

In this correspondence, we consider the class of finite-state Markov channels (FSMCs) in which the channel behaves as a binary symmetric channel (BSC) in each state. Upper bounds on the rate of LDPC codes for reliable communication over this class of FSMCs are found. A simple upper bound for all noninverting FSMCs is first derived. Subsequently, tighter bounds are derived for the special case of Gilbert-Elliott (GE) channels. Tighter bounds are also derived over the class of FSMCs considered. The latter bounds hold almost-surely for any sequence of randomly constructed LDPC codes of given degree distributions. Since the bounds are derived for optimal maximum-likelihood decoding, they also hold for belief propagation decoding. Using the derivations of the bounds on the rate, some lower bounds on the density of parity check matrices for given performance over FSMCs are derived     

Entropy/length profiles, bounds on the minimal covering ofbipartite graphs, and trellis complexity of nonlinear codes

The trellis representation of nonlinear codes is studied from a new perspective. We introduce the new concept of entropy/length profile (ELP). This profile can be considered as an extension of the dimension/length profile (DLP) to nonlinear codes. This elaboration of the DLP, the entropy/length profiles, appears to be suitable to the analysis of nonlinear codes. Additionally and independently, we use well-known information-theoretic measures to derive novel bounds on the minimal covering of a bipartite graph by complete subgraphs. We use these bounds in conjunction with the ELP notion to derive both lower and upper bounds on the state complexity and branch complexity profiles of (nonlinear) block codes represented by any trellis diagram. We lay down no restrictions on the trellis structure, and we do not confine the scope of our results to proper or one-to-one trellises only. The basic lower bound on the state complexity profile implies that the state complexity at any given level cannot be smaller than the mutual information between the past and the future portions of the code at this level under a uniform distribution of the codewords. We also devise a different probabilistic model to prove that the minimum achievable state complexity over all possible trellises is not larger than the maximum value of the above mutual information over all possible probability distributions of the codewords. This approach is pursued further to derive similar bounds on the branch complexity profile. To the best of our knowledge, the proposed upper bounds are the only upper bounds that address nonlinear codes. The novel lower bounds are tighter than the existing bounds. The new quantities and bounds reduce to well-known results when applied to linear codes     

Performance bounds for power control supported DCA-algorithms inhighway micro cellular radio systems

To achieve a high spectrum efficiency in cellular radio systems, the radio resource allocation algorithms have to be adaptive to the actual traffic and interference situation. The focus of the paper is on performance bounds of a cellular radio system using dynamic channel assignment (DCA) combined with power control (PC). A trivial upper bound on the performance is identified. The bound is given by the performance of a hypothetical system which is able to use all channels simultaneously in all cells. A lower bound on the performance is derived from a theoretical PC supported DCA-algorithm. For a highway micro cellular system and a deterministic propagation model, numerical results show that the lower and upper bounds are tight. That is, the results indicate that it is possible to use all channels in all cells simultaneously and still provide an acceptable signal-to interference ratio in all assigned communication links     

一类Feistel密码的线性分析

该文提出一种新的求取分组密码线性偏差上界的方法，特别适用于密钥线性作用的Feistel密码．该分析方法的思路是，首先对密码体制线性偏差进行严格的数学描述，分别给出密码线性偏差与轮函数F及S盒的线性偏差的数学关系；然后通过求取线性方程组最小重量解，确定密码线性偏差的上界．     

Bounds and constructions for codes correcting unidirectional errors

A brief introduction is given on the theory of codes correcting unidirectional errors, in the context of symmetric and asymmetric error-correcting codes. Upper bounds on the size of a code of length n correcting t or fewer unidirectional errors are then derived. Methods in which codes correcting up to t unidirectional errors are constructed by expurgating t-fold asymmetric error-correcting codes or by expurgating and puncturing t -fold symmetric error-correcting codes are also presented. Finally, tables summarizing some results on the size of optimal unidirectional error-correcting codes which follow from these bounds and constructions are given     

Moment space upper and lower error bounds for digital systems with intersymbol interference

A method for the evaluation of upper and lower bounds to the error probability of a linear pulse-amplitude modulation (PAM) system with bounded intersymbol interference and additive Gaussian noise is obtained via an isomorphism theorem from the theory of moment spaces. These upper and lower bounds are seen to be equivalent to upper and lower envelopes of some compact convex body generated from a set of kernel functions. Depending on the selection of these kernels and their corresponding moments, different classes of bounds are obtained. In this paper, upper and lower bounds that depend on the absolute moment of the intersymbol interference random variable, the second moment, the fourth moment, and an "exponential moment" are found by analytical, graphical, or iterative approaches. We study in detail the exponential moment case and obtain a family of new upper and a family of new lower bounds. Within each family, expressions for these bounds are given explicitly as a function of an arbitrary real-valued parameter. For two channels of interest, upper and lower bounds are evaluated and compared. Results indicate these bounds to be tight and useful.     

An improved upper bound on the block coding error exponent for binary-input discrete memoryless channels (Corresp.)

The recent upper bounds on the minimum distance of binary codes given by McEliece, Rodemich, Rumsey, and Welch are shown to result in improved upper bounds on the block coding error exponent for binary-input memoryless channels.     

A new universal random coding bound for the multiple-access channel

The minimum average error probability achievable by block codes on the two-user multiple-access channel is investigated. A new exponential upper bound is found which can be achieved universally for all discrete memoryless multiple-access channels with given input and output alphabets. It is shown that the exponent of this bound is greater than or equal to those of previously known bounds. Moreover, examples are given where the new exponent is strictly larger     

An approach for computing tight numerical bounds on renewalfunctions

This method computes tight lower and upper bounds for the renewal function. It is based on Riemann-Stieltjes integration, and provides bounds for solving certain renewal equations used in the study of availability. An error analysis is given for the numerical bounds when inter-renewal time distributions are sufficiently smooth. Three examples are explored that demonstrate the accuracy of these computed numerical bounds