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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 work we present construction of Space Time Block Codes (STBC) from Abelian codes. A well known Eisenstein-Jacobi rank preserving map is applied to map the codeword matrix symbols to symbols in the complex plane. We then propose an NT × NR MIMO (multiple input, multiple output) communication system employing the constructed STBC. An analysis on the receiver (decoder) computational complexity...
Energy accumulation is an approach to reducing the power consumption of broadcast. In conventional approaches, a node can decode the message if the received power from a single transmission is above a threshold. In contrast, in the cooperative approach based on energy accumulation, a node can decode the message if the sum of the received powers from any set of transmissions exceeds the threshold....
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...
We construct permutation codes capable of correcting bursts of stable deletions. For correcting a single burst of exactly s stable deletions, our code has size sn!/((2s)!n)2 while the upper bound is n!/s!(n − s + 1). We also construct permutation codes for the cases of single burst of up to s stable deletions, and up to b bursts of at most s stable deletions each.
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...
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...
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 error correction by maximum distance separable (MDS) codes based on a part of the received codeword. Our problem is motivated by applications in distributed storage. While efficiently correcting erasures by MDS storage codes (the “repair problem”) has been widely studied in recent literature, the problem of correcting errors in a similar setting seems to represent a new question in coding...
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...
For any code, the set of received words generated by insertion errors is infinitely large. We prove that infinitely many of these words are uniquely decodable. We proceed to analyze how often unique decoding from insertions occurs for arbitrary codes. These questions are relevant because insertion errors frequently occur in synchronization and DNA, a medium which is beginning to be used for long term...
“To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.” We show that the reliable communication through a classical-quantum channel is possible when the transmission rate approaches the channel capacity sufficiently slowly. This scenario exists between the non-vanishing error probability regime, where the rate tends to capacity with a fixed error, and the small error probability...
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...
The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analog-to-digital converter (ADC). It is proved that the input distributions that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of...
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 problem of characterizing sufficient conditions for communicating correlated sources over a MAC is considered. The technique of inducing source correlation onto channel inputs [1] is enhanced by the use of fixed B-L coding [2]. The performance of the proposed coding technique is characterized via single-letter expressions to derive a new set of sufficient conditions. The latter conditions are...
List decoding of insertions and deletions in the Levenshtein metric is considered. In this paper, a Johnson-like upper bound on the maximum list size when decoding in the Levenshtein metric is derived. This bound depends only on the length and minimum Levenshtein distance of the code, the length of the received word, and the alphabet size. It shows that polynomial-time list decoding beyond half the...
We consider Bernoulli nonadaptive group testing with k = Θ(ηθ) defectives, for θ ∊ (0,1). The practical definite defectives (DD) detection algorithm is known to be optimal for θ > 1/2. We give a new upper bound on the rate of DD, showing that DD is strictly suboptimal for θ < 0.41. We also show that the SCOMP algorithm and algorithms based on linear programming achieve a rate at least as high...
Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a specific intrinsic-state distribution. In this paper we study the maximum and the minimum capacities of a channel when the realization of its intrinsic state is causally...
This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Rényi conditional entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon conditional entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano's inequality...
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