Related papers: Energy, Latency, and Reliability Tradeoffs in Codi…
Thompson's model of VLSI computation relates the energy of a computation to the product of the circuit area and the number of clock cycles needed to carry out the computation. It is shown that for any family of circuits implemented…
It is shown that all polar encoding schemes of rate $R>\frac{1}{2}$ of block length $N$ implemented according to the Thompson VLSI model must take energy $E\ge\Omega\left(N^{3/2}\right)$. This lower bound is achievable up to polylogarithmic…
It is shown that in a sequence of randomly generated bipartite configurations with number of left nodes approaching infinity, the probability that a particular configuration in the sequence has a minimum bisection width proportional to the…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
The free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, free energy has finite size…
Dealing with the shear size and complexity of today's massive data sets requires computational platforms that can analyze data in a parallelized and distributed fashion. A major bottleneck that arises in such modern distributed computing…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is…
We consider the problem of computing a binary linear transformation using unreliable components when all circuit components are unreliable. Two noise models of unreliable components are considered: probabilistic errors and permanent errors.…
It has been established that when the gradient coding problem is distributed among $n$ servers, the computation load (number of stored data partitions) of each worker is at least $s+1$ in order to resists $s$ stragglers. This scheme incurs…
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
This paper characterizes the trade-offs between information and energy transmission over an additive white Gaussian noise channel in the finite block-length regime with finite channel input symbols. These trade-offs are characterized in the…
Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
Recently, a parallel decoding framework of $G_N$-coset codes was proposed. High throughput is achieved by decoding the independent component polar codes in parallel. Various algorithms can be employed to decode these component codes,…
Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for…
Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently,…
Term Coding asks: given a finite system of term identities $\Gamma$ in $v$ variables, how large can its solution set be on an $n$--element alphabet, when we are free to choose the interpretations of the function symbols? This turns familiar…
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed. Given a tradeoff between $N,P$…