We consider the problem of encoding an i.i.d. source into a set of symbols or messages that may be altered by an adversary while en route to the decoder. We focus in particular on the regime in which the number of messages is fixed while the blocklength of the source and the size of each message tend to infinity. For this fixed-blocklength, “large alphabet” channel, we show that combining an optimal rate-distortion code with an optimal error-correction code yields an optimal overall code for Gaussian sources with quadratic distortion and binary uniform sources with Hamming distortion but that it can be suboptimal by an arbitrarily large factor in general. We also consider the scenario in which the distortion constraint that the decoder must satisfy depends on the number of errors that occur. We show that the problem can be reduced operationally to one with erasures instead of errors in two special cases: one involving lossless reproduction of functions of the source and one in which the encoder and decoder share common randomness.

Coding for the Large-Alphabet Adversarial Channel

In a Diversity Coding System, an information source is is encoded by a number of encoders. There are a number of decoders, each of which can access a certain subset of the encoders. In this paper, we study a diversity coding problem in which there are two levels of decoders. The reconstructions of the source by decoders within the same level are identical, and are subject to the same distortion criterion. Our results imply a principle of superposition when the source consists of two independent data streams. Practical codes achieving zero error can easily be constructed for this special case. A class of open problems on this topic is also suggested

Multilevel diversity coding with distortion

We consider a problem in which a source is encoded into N packets, an unknown number of which are subject to adversarial errors en route to the decoder. We seek code designs for which the decoder is guaranteed to be able to reproduce the source subject to a certain distortion constraint when there are no packets errors, subject to a less stringent distortion constraint when there is one error, etc. Focusing on the special case of the erasure distortion measure, we introduce a code design based on the polytope codes of Kosut, Tong, and Tse. The resulting designs are also applied to a separate problem in distributed storage.

Variable Packet-Error Coding

We consider a problem in which a source is encoded into $N$ packets, an unknown number of which are subject to adversarial errors en route to the decoder. We seek code designs for which the decoder is guaranteed to be able to reproduce the source subject to a certain distortion constraint when there are no packets errors, subject to a less stringent distortion constraint when there is one error, and so on. Focusing on the special case of the erasure distortion measure, we introduce a code design based on the polytope codes of Kosut et al. . The resulting designs are also applied to a separate problem in distributed storage.

Dynamic vehicle routing with random requests: A literature review

Motivated by packet networks, we consider channels for which the blocklength is short, the input and output alphabets are large, and the transmitted symbols are subject to adversarial errors. Most work on channel coding for adversarial errors assumes that the number of errors is upper bounded by a known constant, and the code designs do not provide an improved performance guarantee should the actual number of errors be below this constant. We develop designs for which the source to be transmitted is recovered perfectly when there are no errors and partially, but correctly, when errors are introduced. Our main design is based on the polytope code design of Kosut, Tong, and Tse.

Polytope codes for large-alphabet channels

We consider the problem of communicating a Gaussian source over several paths in a network, some unknown subset of which are subject to adversarial errors. The aim is to encode the source in such a way that one can provide a mean-square error distortion guarantee at the receiver that improves as the number of path-errors decreases. We show that a natural design based on error-correcting and error-detecting codes is not order-optimal in the rate as the distortion constraint tends to zero, but a hybrid scheme that involves a form of uncoded transmission is.

Gaussian variable packet-error coding

We consider a communication problem in which a transmitter encodes a source into several streams that are subject to modification by an omniscient adversary while en route. We design encodings with a distortion guarantee that degrades gradually as the number of streams that the adversary alters increases. Notably, we find that a mixture of highly redundant coding and uncoded transmission outperforms schemes that protect all of the transmitted data against adversarial attack. This finding is confirmed both theoretically and experimentally.

Xiaoqing Fan

Papers

Polytope codes for large-alphabet channels

Variable Packet-Error Coding

Variable Packet-Error Coding

Gaussian variable packet-error coding

Resilient communication against adversarial path-errors