Iris Code Capacity Analysis

Daugman’s design of IrisCode continues fascinating the research world with its practicality, efficiency, and outstanding performance. The limits of Daugman’s recognition system, however, remain unquantified. Multiple approaches to scale performance have been explored in the past. Despite them, the problem of finding the capacity of IrisCode remains open.<br>In an attempt to fill the gap in understanding the performance limits of Daugman’s algorithm, we turn to an analysis of the relationship between the size of the population that the IrisCode can effectively cover and the iris sample quality. Given Daugman’s IrisCode algorithm, the problem of finding its capacity is cast as a basic Rate-Distortion/Channel Coding problem. The Hamming, Plotkin, and Elias-Bassalygo upper bounds on the population of a binary code under the constraint of a minimum Hamming Distance between any two codewords is applied to relate the number of iris classes that the IrisCode algorithm can sustain and the quality of iris data expressed in terms of Hamming Distance.<br><br>

Iris Code Capacity Analysis

Daugman’s design of IrisCode continues fascinating the research world with its practicality, efficiency, and outstanding performance. The limits of Daugman’s recognition system, however, remain unquantified. Multiple approaches to scale performance have been explored in the past. Despite them, the problem of finding the capacity of IrisCode remains open.<br>In an attempt to fill the gap in understanding the performance limits of Daugman’s algorithm, we turn to an analysis of the relationship between the size of the population that the IrisCode can effectively cover and the iris sample quality. Given Daugman’s IrisCode algorithm, the problem of finding its capacity is cast as a basic Rate-Distortion/Channel Coding problem. The Hamming, Plotkin, and Elias-Bassalygo upper bounds on the population of a binary code under the constraint of a minimum Hamming Distance between any two codewords is applied to relate the number of iris classes that the IrisCode algorithm can sustain and the quality of iris data expressed in terms of Hamming Distance.<br><br>

Low Density Parity-Check Codes Based on Affine Permutation Matrices

Recently, Low Density Parity-Check (LDPC) codes based on Affine Permutation Matrices (APM) drew lots of attention. Compared with the Quasi-Cyclic LDPC (QC-LDPC) codes, these kinds of codes have some advantages. APM-LDPC codes obtain lower cycle-distributions, minimum hamming distance and greater girth. This paper explains the importance of cyclic distribution by comparing APM-LDPC codes with QC-LDPC codes. Then a particular form of APM-LDPC codes is proposed and researched. The new codes can low down the cycle-distribution to larger extent. In the following research, an effective method, which constructs the new codes with fixed girth, is proposed. Simulations show that the construction method is reasonable and effective. The transmission performances are better than the traditional methods, as well. Finally, the implementation and verification are carried out on FPGA.

On the Stability and Instability of Finite Dynamical Systems with Prescribed Interaction Graphs

The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding, and in the context of hat games, such as the guessing game and Winkler's hat game. The instability of an FDS is the minimum Hamming distance between a state and its image under the FDS, while the stability is the minimum of the reciprocal of the Hamming distance; they are both directly related to Winkler's hat game. In this paper, we study the value of the (in)stability of FDSs with prescribed interaction graphs. The first main contribution of this paper is the study of the maximum stability for interaction graphs with a loop on each vertex. We determine the maximum (in)stability for large enough alphabets and also prove some lower bounds for the Boolean alphabet. We also compare the maximum stability for arbitrary functions compared to monotone functions only. The second main contribution of the paper is the study of the average (in)stability of FDSs with a given interaction graph. We show that the average stability tends to zero with high alphabets, and we then investigate the average instability. In that study, we give bounds on the number of FDSs with positive instability (i.e fixed point free functions). We then conjecture that all non-acyclic graphs will have an average instability which does not tend to zero when the alphabet is large. We prove this conjecture for some classes of graphs, including cycles.

Fat points, partial intersections and Hamming distance

We use two main techniques, namely, residuation and separators of points, to show that the Hilbert function of a certain fat point set supported on a grid complete intersection is the same as the Hilbert function of a reduced set of points called a partial intersection. As an application, we answer a question of Tohǎneanu and Van Tuyl which relates the minimum Hamming distance of a special linear code and the minimum socle degree of the associated fat point set.

New Binary Locally Repairable Codes with Locality 2 and Uneven Availabilities for Hot Data

In this paper, a new family of binary LRCs (BLRCs) with locality 2 and uneven availabilities for hot data is proposed, which has a high information symbol availability and low parity symbol availabilities for the local repair of distributed storage systems. The local repair of each information symbol for the proposed codes can be done not by accessing other information symbols but only by accessing parity symbols. The proposed BLRCs with k = 4 achieve the optimality on the information length for their given code length, minimum Hamming distance, locality, and availability in terms of the well-known theoretical upper bound.

On Zeros of a Polynomial in a Finite Grid

A 1993 result of Alon and Füredi gives a sharp upper bound on the number of zeros of a multivariate polynomial over an integral domain in a finite grid, in terms of the degree of the polynomial. This result was recently generalized to polynomials over an arbitrary commutative ring, assuming a certain ‘Condition (D)’ on the grid which holds vacuously when the ring is a domain. In the first half of this paper we give a further generalized Alon–Füredi theorem which provides a sharp upper bound when the degrees of the polynomial in each variable are also taken into account. This yields in particular a new proof of Alon–Füredi. We then discuss the relationship between Alon–Füredi and results of DeMillo–Lipton, Schwartz and Zippel. A direct coding theoretic interpretation of Alon–Füredi theorem and its generalization in terms of Reed–Muller-type affine variety codes is shown, which gives us the minimum Hamming distance of these codes. Then we apply the Alon–Füredi theorem to quickly recover – and sometimes strengthen – old and new results in finite geometry, including the Jamison–Brouwer–Schrijver bound on affine blocking sets. We end with a discussion of multiplicity enhancements.