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The problem of analyzing the finite-length scaling behavior of sparse random linear codes is considered. Random linear codes with random generator matrices whose entries are picked according to i.i.d. Bernoulli distribution with parameter q = o(1) are called sparse. The parameter q is referred to as the sparsity of the random linear code. We develop a methodology to show the optimality of the scaling...
We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding algorithm for the codes that finds a close codeword to a given random word. We provide both theoretical analysis of the performance and stability of the decoding algorithm,...
We give a length-efficient puncturing of Reed-Muller codes which preserves its distance properties. Formally, for the Reed-Muller code encoding n-variate degree-d polynomials over F_q with q gtrsim d/delta, we present an explicit (multi)-set S subseteq F_q^n of size N=mathrm {poly}(n^d/delta) such that every nonzero polynomial vanishes on at most delta N points in S. Equivalently, we give an explicit...
Extending Delsarte's linear programming bound for error correcting codes, this paper obtains a linear programming bound for locally repairable storage codes. The number of variables involved in the bound scales linearity with the size of the code. The bound can also be viewed as a necessary condition for the existence of a storage code and be used to characterise the tradeoff among the costs for storage,...
The problem of designing codes to protect against server failures in a distributed storage system for frequently changing data is considered. When the original data changes, the coded packets stored on the servers must be updated accordingly. Since performing updates consumes costly bandwidth and energy, it is of interest to construct codes that have small update complexity, which we define as the...
We consider the constructions of tail-biting trellises for linear codes introduced by Koetter/Vardy and Nori/Shankar. We will show that each one-to-one product trellis can be merged to a BCJR-trellis defined in a slightly stronger sense than in and that each trellis that originates from the characteristic matrix defined in is a BCJR-trellis. Furthermore, BCJR-trellises are always nonmergeable. Finally,...
We present a class of algorithms for encoding data in memories with stuck cells. These algorithms rely on earlier code constructions termed cyclic Partitioned Linear Block Codes. For the corresponding q-ary BCH-like codes for u stucks in a codeword of length n, our encoding algorithm has complexity O((u logq n)2) Fq operations, which we will show compares favorably to a generic approach based on Gaussian...
Cognitive radio is an emerging technology that allows secondary communication in a frequency band originally allocated to one or more primary users (PUs). Secondary user (SU) usually operates in a low power profile to avoid interference with the PU and sudden appearance of a PU causes loss of data of the SU. Appropriate erasure correction coding (also called as anti-jamming coding) is, thus, required...
The low decoding complexity structure of Linear Dispersion Space Time Block Codes (LDSTBCs) with unitary weight matrices is analyzed. It is shown that given n = 2alpha, the maximum number of groups in which the information symbols can be separated and decoded independently is (2a + 2), and as we lower the number of different groups to (2k + 2), 0 les k les alpha, we get higher rate codes. We also...
A twofold multilevel concatenated coding scheme is proposed. The multilevel coding structure is based on set partitioning of an expanded set of interlevel-correlated multilevel coset codes. We can design a variety of binary linear block codes with high coding gain and low decoding complexity.
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