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The emergence of large-scale dynamic sets in real applications creates stringent requirements for approximate set representation structures: 1) the capacity of the set representation structures should support flexibly extending or reducing to cope with dynamically changing of set size; 2) the set representation structures should support reliable delete operation. Existing techniques for approximate...
In cloud storage systems, the use of erasure coding results in high read latency and long recovery time when drive or node failure happens. In this paper, we design a parity independent array codes (PIT), a variation of STAR code, which is triple fault tolerant and nearly space-optimal, and also propose an efficient single-failure recovery scheme (PITR) for them to mitigate the problem. In addition,...
In this paper wireless communications network is considered to transmit source information to destination. N number sources transmitting data to a destination receiver, through M relays nodes by employing random linear network coding (RLNC). Two methods of failure decoding probability on performance of wireless communication are explained and discussed in this paper. The major parameter that will...
Recently Yamamoto and Ueda proposed multiple object identification (MOID) codes to identify multiple objects via a channel at once, which is an extension of identification (ID) codes. They gave the explicit construction of MOID codes and derived the achievable triplet of coding rate R, the error exponents E1 and E2 of type I and type II decoding error probabilities. However, they did not treat the...
Improved lower bounds on the worst-case and the average-case rate-memory tradeoffs for the Maddah-Ali&Niesen coded-caching scenario are presented. For any number of users and files and for arbitrary cache sizes, the multiplicative gap between the exact rate-memory tradeoff and the new lower bound is less than 2.315 in the worst-case scenario and less than 2.507 in the average-case scenario.
We consider the problem of polar coding for transmission over a non-stationary sequence of independent binary-input memoryless symmetric (BMS) channels {Wi}∞i=1 where the i-th encoded bit is transmitted over Wi. We show, for the first time, a polar coding scheme that achieves the average symmetric capacity Ī({Wi}∞i=1) def= limN→∞ 1/N NΣi=1 I(Wi) assuming that the limit exists. The polar coding scheme...
This paper investigates the achievable rates of an additive white Gaussian noise (AWGN) energy-harvesting (EH) channel with an infinite battery under the assumption that the error probabilities do not vanish as the blocklength increases. The EH process is characterized by a sequence of blocks of harvested energy. The harvested energy remains constant within a block while the harvested energy across...
In this work, we establish the pointwise optimality of side information version of SWLZ algorithm for stationary ergodic sources. We also obtain a pointwise upper bound on the redundancy rate of this side information version of SWLZ algorithm for a subclass of φ-mixing sources, which includes Markov sources as a special case. This upper bound obtained differs only by a constant factor from the best...
We consider the broadcasting of a single Gaussian source over a two-user Gaussian broadcast channel with bandwidth expansion. In addition to the source broadcasting the encoder sends a message reliably to the “higher quality” user. Conditioned on the message rate, we derive an outer bound on the set of attainable mean-squared error distortion pairs at the two users which extends the Reznic-Feder-Zamir...
Write-once memory (WOM) is a storage device consisting of binary cells which can only increase their levels. A t-write WOM code is a coding scheme which allows to write t times to the WOM without decreasing the levels of the cells. The sum-rate of a WOM code is the ratio between the total number of bits written to the memory and the number of cells. It is known that the maximum sum-rate of a t-write...
It is now well known that using a long and complicated error correcting code (ECC) designed for the worst-case error probability requirement wastes excessive total system energy (transmit + circuit energy) when the error probability requirement is much higher than the worst case. We propose a novel adaptive polar coding strategy that adjusts the decoder circuit to consume minimal decoding circuit...
A concatenated coding scheme using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first bound is obtained using outer codes which are typical linear codes from the ensemble of parity check matrices whose elements are chosen independently and uniformly. As a byproduct of this bound, it determines...
The index coding problem is a problem of efficient broadcasting with side-information. In uniprior index coding, the sets of side-information symbols possessed by different receivers are disjoint. For single uniprior index coding, in which each receiver has a single unique side-information symbol, a polynomial complexity construction of an optimal index code is known from prior work. In this work,...
The degraded K-receiver broadcast channel (BC) is studied when receivers are aided with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate that can be achieved as a function of the receivers' cache sizes. The lower bounds are achieved by two new coding schemes that benefit from non-uniform cache assignment. The paper also provides lower and...
X-codes are linear maps with a special combinatorial property that generalizes superimposed codes, disjunct matrices, and cover-free families. In the context of circuit testing, a (t, n, d, x) X-code compresses n-bit output from the circuit under test into t bits while allowing for detecting the existence of up to d erroneous output bits even if up to x bits of the correct behavior are unknowable...
Mutually Uncorrelated (MU) codes are a class of codes in which no proper prefix of one codeword is a suffix of another codeword. These codes were originally studied for synchronization purposes and recently, Yazdi et al. showed their applicability to enable random access in DNA storage. In this work we follow the research of Yazdi et al. and study MU codes along with their extensions to correct errors...
Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to maintain reliability in reading and writing, new coding schemes must be developed. In a reading technique called shotgun sequencing, a long DNA string is read in...
The problem of constructing sticky-insertion-correcting codes with efficient encoding and decoding is considered. An {n, M, r) sticky-insertion-correcting code consists of M codewords of length n such that any pattern of up to r sticky insertions can be corrected. We utilize BCH codes and their analogous in the Lee space to construct explicit and systematic codes that are immune to up to r sticky...
The downlink of symmetric Cloud Radio Access Networks (C-RANs) with multiple relays and a single receiver is studied. Lower and upper bounds are derived on the capacity. The lower bound is achieved by Marton's coding which facilitates dependence among the multiple-access channel inputs. The upper bound uses Ozarow's technique to augment the system with an auxiliary random variable. The bounds are...
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