Binary symmetric channel | EPFL Graph Search

A binary symmetric channel (or BSCp) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability" of p, and otherwise is received correctly. This model can be applied to varied communication channels such as telephone lines or disk drive storage. The noisy-channel coding theorem applies to BSCp, saying that information can be transmitted at any rate up to the channel capacity with arbitrarily low error. The channel capacity is 1 - \operatorname H_\text{b}(p) bits, where \operatorname H_\text{b} is the binary entropy function. Codes including Forney's code have been designed to transmit information efficiently across the channel. Definition A binary symmetric channel with crossover probability p, denoted by BSCp, is a channel with binary input and

Feedback communication over unknown channels

Aslan Tchamkerten

Suppose Q is a family of discrete memoryless channels. An unknown member of Q will be available, with perfect, causal output feedback for communication. Is there a coding scheme (possibly with variable transmission time) that can achieve the Burnashev error exponent uniformly over Q ? For two families of channels we show that the answer is yes. Furthermore, for each of these two classes, in addition to achieve the maximum error exponent, it is possible to uniformly attain any given fraction of the channel capacity. Therefore, in terms of achievable rates and delay, there are situations in which the knowledge of the channel becomes irrelevant. In the second part of the thesis, we show that for arbitrary sets of channels the Burnashev error exponent cannot in general be uniformly achieved. In particular we give a sufficient condition for a pair of channels so that no coding strategy reaches Burnashev's exponent simultaneously on both channels. As a third part we study a scenario where communication is carried by first testing the channel by means of a training sequence, then coding according to the channel estimate. We provide an upper bound on the maximum achievable error exponent of such coding schemes. This bound is typically much lower than the maximum achievable error exponent over a channel with feedback. For example in the case of binary symmetric channels this bound has a slope that vanishes at capacity. This result suggests that in terms of error exponent, a good universal feedback scheme combines channel estimation with information delivery, rather than separating them. In the final chapter, we address the question of communicating quickly and reliably. We consider a simple situation of two message communication over a known channel with feedback. We propose a simple decoding rule, and show that it minimizes a weighted combination of the probability of error and decoding delay for a certain range of crossover probabilities and combination weights.

EPFL2005

On the use of training sequences for channel estimation

Aslan Tchamkerten, Emre Telatar

Suppose Q is a family of discrete memoryless channels. An unknown member of Q is available with perfect (causal) feedback for communication. A recent result (A. Tchamkerten and I.E. Telatar) shows the existence, for certain families of channels (e.g. binary symmetric channels and Z channels), of coding schemes that achieve Burnashev's exponent universally over these families. In other words, in certain cases, there is no loss in the error exponent by ignoring the channel: transmitter and receiver can design optimal blind coding schemes that perform as well as the best feedback coding schemes tuned for the channel under use. Here we study the situation where communication is carried by first testing the channel by means of a training sequence, then coding the information according to the channel estimate. We provide an upper bound on the maximum achievable error exponent of any such scheme. If we consider binary symmetric channels and Z channels this bound is much lower than Burnashev's exponent. This suggests that in terms of error exponent, a good universal feedback scheme entangles channel estimation with information delivery, rather than separating them.

2005

On the universality of Burnashev's error exponent

Aslan Tchamkerten, Emre Telatar

We consider communication over a time-invariant discrete memoryless channel (DMC) with noiseless and instantaneous feedback. We assume that the transmitter and the receiver are not aware of the underlying channel, however, they know that it belongs to some specific family of DMCs. Recent results show that for certain families (e.g., binary-symmetric channels and Z channels) there exist coding schemes that universally achieve any rate below capacity while attaining Burnashev's error exponent. We show that this is not the case in general by deriving an upper bound to the universally achievable error exponent.

2005

Feedback communication over unknown channels

Aslan Tchamkerten

EPFL2005