Optimal Error Rates for Interactive Coding I: Adaptivity and Other Settings

We consider the task of interactive communication in the presence of adversarial errors and present tight bounds on the tolerable error-rates in a number of different settings. Most significantly, we explore adaptive interactive communication where the communicating parties decide who should speak next based on the history of the interaction. Braverman and Rao [STOC'11] show that non-adaptively one can code for any constant error rate below 1/4 but not more. They asked whether this bound could be improved using adaptivity. We answer this open question in the affirmative (with a slightly different collection of resources): Our adaptive coding scheme tolerates any error rate below 2/7 and we show that tolerating a higher error rate is impossible. We also show that in the setting of Franklin et al. [CRYPTO'13], where parties share randomness not known to the adversary, adaptivity increases the tolerable error rate from 1/2 to 2/3. For list-decodable interactive communications, where each party outputs a constant size list of possible outcomes, the tight tolerable error rate is 1/2. Our negative results hold even if the communication and computation are unbounded, whereas for our positive results communication and computation are polynomially bounded. Most prior work considered coding schemes with linear amount of communication, while allowing unbounded computations. We argue that studying tolerable error rates in this relaxed context helps to identify a setting's intrinsic optimal error rate. We set forward a strong working hypothesis which stipulates that for any setting the maximum tolerable error rate is independent of many computational and communication complexity measures. We believe this hypothesis to be a powerful guideline for the design of simple, natural, and efficient coding schemes and for understanding the (im)possibilities of coding for interactive communications

Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding

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. Important performance measures for a coding scheme are its maximum tolerable error rate $\rho$, communication complexity $N$, and computational complexity. We give the first coding scheme for the standard setting which performs optimally in all three measures: Our randomized non-adaptive coding scheme has a near-linear computational complexity and tolerates any error rate $\delta < 1/4$ with a linear $N = \Theta(n)$ communication complexity. This improves over prior results which each performed well in two of these measures. We also give results for other settings of interest, namely, the first computationally and communication efficient schemes that tolerate $\rho < \frac{2}{7}$ adaptively, $\rho < \frac{1}{3}$ if only one party is required to decode, and $\rho < \frac{1}{2}$ if list decoding is allowed. These are the optimal tolerable error rates for the respective settings. These coding schemes also have near linear computational and communication complexity. These results are obtained via two techniques: We give a general black-box reduction which reduces unique decoding, in various settings, to list decoding. We also show how to boost the computational and communication efficiency of any list decoder to become near linear.Comment: preliminary versio

Multi-hop Byzantine reliable broadcast with honest dealer made practical

We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g., digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment

Cache Serializability: Reducing Inconsistency in Edge Transactions

Read-only caches are widely used in cloud infrastructures to reduce access latency and load on backend databases. Operators view coherent caches as impractical at genuinely large scale and many client-facing caches are updated in an asynchronous manner with best-effort pipelines. Existing solutions that support cache consistency are inapplicable to this scenario since they require a round trip to the database on every cache transaction. Existing incoherent cache technologies are oblivious to transactional data access, even if the backend database supports transactions. We propose T-Cache, a novel caching policy for read-only transactions in which inconsistency is tolerable (won't cause safety violations) but undesirable (has a cost). T-Cache improves cache consistency despite asynchronous and unreliable communication between the cache and the database. We define cache-serializability, a variant of serializability that is suitable for incoherent caches, and prove that with unbounded resources T-Cache implements this new specification. With limited resources, T-Cache allows the system manager to choose a trade-off between performance and consistency. Our evaluation shows that T-Cache detects many inconsistencies with only nominal overhead. We use synthetic workloads to demonstrate the efficacy of T-Cache when data accesses are clustered and its adaptive reaction to workload changes. With workloads based on the real-world topologies, T-Cache detects 43-70% of the inconsistencies and increases the rate of consistent transactions by 33-58%.Comment: Ittay Eyal, Ken Birman, Robbert van Renesse, "Cache Serializability: Reducing Inconsistency in Edge Transactions," Distributed Computing Systems (ICDCS), IEEE 35th International Conference on, June~29 2015--July~2 201

Rank-based camera spectral sensitivity estimation

In order to accurately predict a digital camera response to spectral stimuli, the spectral sensitivity functions of its sensor need to be known. These functions can be determined by direct measurement in the lab—a difficult and lengthy procedure—or through simple statistical inference. Statistical inference methods are based on the observation that when a camera responds linearly to spectral stimuli, the device spectral sensitivities are linearly related to the camera rgb response values, and so can be found through regression. However, for rendered images, such as the JPEG images taken by a mobile phone, this assumption of linearity is violated. Even small departures from linearity can negatively impact the accuracy of the recovered spectral sensitivities, when a regression method is used. In our work, we develop a novel camera spectral sensitivity estimation technique that can recover the linear device spectral sensitivities from linear images and the effective linear sensitivities from rendered images. According to our method, the rank order of a pair of responses imposes a constraint on the shape of the underlying spectral sensitivity curve (of the sensor). Technically, each rank-pair splits the space where the underlying sensor might lie in two parts (a feasible region and an infeasible region). By intersecting the feasible regions from all the ranked-pairs, we can find a feasible region of sensor space. Experiments demonstrate that using rank orders delivers equal estimation to the prior art. However, the Rank-based method delivers a step-change in estimation performance when the data is not linear and, for the first time, allows for the estimation of the effective sensitivities of devices that may not even have “raw mode.” Experiments validate our method