Tight Performance Bounds for Permutation Invariant Binary Linear Block Codes Over Symmetric Channels

Xenoulis, Kostis; Kalouptsidis, N.

doi:10.1109/tit.2011.2162176

Cited by 3 publications

(10 citation statements)

References 29 publications

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“…The present paper extends the work in [14] with the introduction of the class of q-ary L-list permutation invariant linear codes and the analysis of the error performance of its members under list decoding for transmission over q-ary discrete symmetric memoryless channels. Towards the extension of list permutation invariant codes from binary to q-ary fields and in comparison to [14], a new definition of L-list permutation invariant codes is provided in order to address a broader class of candidate codes.…”

Section: Introductionmentioning

confidence: 73%

“…Proof: The proof of the lemma follows the same line as in the proof of [14,Lemma 1]. In particular, suppose that in the original L-list permutation invariant code C the received vector is y ∈ Y L 0,C where the weight distribution of the unique coset y−C is { ν,w } N w=0 .…”

Section: Permutation Invariancementioning

confidence: 98%

“…As in [14], from an L-list permutation invariant linear code C we create an ensemble of linear codes E by considering all possible position permutation codes PC. A PC code is constructed by multiplying every codeword of C with a N × N position permutation matrix P which has a single 1 in every row and column and is orthogonal, PP T = P T P = I , where I is the N × N identity matrix and P T the transpose matrix of P. The permutation ensemble E is utilized in order to prove the following property for an L-list permutation invariant linear code.…”

Section: Permutation Invariancementioning

confidence: 99%

“…The double exponential technique, as described in the previous paragraph, is relative new and has appeared in [14]. In general, double exponential bounds have appeared in the analysis of error exponents for channels with feedback, such as in [15] and references therein, but are not related to the presented technique.…”

Section: Introductionmentioning

confidence: 99%

“…Towards the extension of list permutation invariant codes from binary to q-ary fields and in comparison to [14], a new definition of L-list permutation invariant codes is provided in order to address a broader class of candidate codes. Even though the extension to the general q-ary case is straightforward, the derivation of an analytic error bound expression is rather complicated.…”

Section: Introductionmentioning

confidence: 99%

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List Permutation Invariant Linear Codes: Theory and Applications

Xenoulis

2014

IEEE Trans. Inform. Theory

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The class of q-ary list permutation invariant linear codes is introduced in this paper along with probabilistic arguments that validate their existence when certain conditions are met. The specific class of codes is characterized by an upper bound that is tighter than the generalized Shulman-Feder bound and relies on the distance of the codes' weight distribution to the binomial (multinomial, respectively) one. The bound applies to cases where a code from the proposed class is transmitted over a q-ary output symmetric discrete memoryless channel and list decoding with fixed list size is performed at the output. In the binary case, the new upper bounding technique allows the discovery of list permutation invariant codes whose upper bound coincides with sphere-packing exponent. Furthermore, the proposed technique motivates the introduction of a new class of upper bounds for general q-ary linear codes whose members are at least as tight as the DS2 bound as well as all its variations for the discrete channels treated in this paper.

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Section: Introductionmentioning

confidence: 73%

Section: Permutation Invariancementioning

confidence: 98%

Section: Permutation Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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List Permutation Invariant Linear Codes: Theory and Applications

Xenoulis

2014

IEEE Trans. Inform. Theory

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An efficient encoding and decoding algorithm for tracking circulation of commodity by discretizing information matrix

Wan

Tong

2016

Int J Numerical Modelling

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SUMMARYIn this paper, an efficient encoding and decoding algorithm is developed for tracking circulation of commodity. We take a discrete and optimized approach to construct the encoding and decoding method by using a matrix as an information carrier. This method is more durable against the damage of outer packages and can obtain a high recovery rate of commodity's information. Generally, it is very diffcult to track the original information in the circulation of commodity. We use the optimized encoding method to link the original information of commodity with a database so that the commodity can be pinpointed in the whole circulation. Also, the original information can be restored by an efficient decoding algorithm whenever necessary. The optimized method is designed based on two traditional encoding and decoding methods, and these methods are compared by running certain simulations with a large number of testing data. The results show that the improved and optimized method can obtain a much higher recovery rate of commodity's information and is more durable against the damage of outer packages.

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Θεωρία Πληροφορίας Και Επεξεργασία Σήματος Για (Μη-Γραμμικά) Επικοινωνιακά Κανάλια

Ξενούλης¹

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Information Theory answers the fundamental problem of communication, that of reproducing at one point either exactly or approximately a message selected at another point. The design and development of synchronous communication systems, like satellite, wireless or optical fibers, rely nowadays in the establishment of performance measure indicators such as the error decoding probability and the channel capacity. Further progress in the field of communications requires among others the development of new, tight performance bounds, that are capable of designating desirable characteristics for coding schemes. The asymptotic behavior of these bounds is not always desirable since they do not reveal practical codes of finite length for simple and more complicated (nonlinear) channel models. Furthemore, the treatment of the inherent nonlinear behaviour of communication systems as well as the calculation of the capacity of the corresponding channels is crucial for enhancing system performance.In this thesis, Gallager's upper bound as well as its variations through the Duman-Salehi bound are improved. The technique that yields this improvement relies on the new inverse exponential sum inequality. The specific criterion is applied to linear codes that are transmitted in discrete, memoryless, linear symmetric channels and upper bounds the word and bit maximum likelihood error decoding probabilities. The analysis designates a new desirable characteristic for linear codes, that is directly connected with the concept of list decoding.The thesis also presents lower bounds on the capacity of nonlinear channels, combining the random coding technique with the theory of martingales. Upper bounds for the maximum likelihood error decoding probability are obtained through the representation of a nonlinear channel with Volterra series. The proposed research follows the main ideas that dominate Shannon's basic work and properly utilizes exponential martingale inequalities in order to bound the probabilities of erroneous decoding regions. The specific analysis is also applied to cases where the noise statistical characteristics (mean value, deviation) remain unknown.A desirable characteristic of the proposed techniques that provide tight bounds for error decoding probability is their ability to designate codes with optimum characteristics and with rates near channel capacity. The present work improves and extends the bound of Shulman-Feder for the family of binary, linear codes that are permutation invariant under list decoding. A new upper bound on list error decoding probability is presented that decreases double exponentially with respect to the code's block length.

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Tight Performance Bounds for Permutation Invariant Binary Linear Block Codes Over Symmetric Channels

Abstract: Index Terms-Double exponential function, L-list permutation invariant codes, list decoding error probability, reliability function.

Cited by 3 publications

References 29 publications

List Permutation Invariant Linear Codes: Theory and Applications

List Permutation Invariant Linear Codes: Theory and Applications

An efficient encoding and decoding algorithm for tracking circulation of commodity by discretizing information matrix

Θεωρία Πληροφορίας Και Επεξεργασία Σήματος Για (Μη-Γραμμικά) Επικοινωνιακά Κανάλια

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