We develop and analyze low-complexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals' relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplify-and-forward and decode-and-forward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signal-to-noise ratio (SNR) regime. Except for fixed decode-and-forward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., second-order diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to half-duplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks-wherever space constraints preclude the use of physical arrays-the performance characterizations reveal that large power or energy savings result from the use of these protocols.

Cooperative diversity in wireless networks: Efficient protocols and outage behavior

We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be multicast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. We study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the max-flow min-cut theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.

http://www.inf.fu-berlin.de/lehre/WS11/Wireless/papers/CodAhlswede00.pdf

Network information flow

A relay channel consists of an input x_{l} , a relay output y_{1} , a channel output y , and a relay sender x_{2} (whose transmission is allowed to depend on the past symbols y_{1} . The dependence of the received symbols upon the inputs is given by p(y,y_{1}|x_{1},x_{2}) . The channel is assumed to be memoryless. In this paper the following capacity theorems are proved. 1)If y is a degraded form of y_{1} , then C \: = \: \max \!_{p(x_{1},x_{2})} \min \,{I(X_{1},X_{2};Y), I(X_{1}; Y_{1}|X_{2})} . 2)If y_{1} is a degraded form of y , then C \: = \: \max \!_{p(x_{1})} \max_{x_{2}} I(X_{1};Y|x_{2}) . 3)If p(y,y_{1}|x_{1},x_{2}) is an arbitrary relay channel with feedback from (y,y_{1}) to both x_{1} \and x_{2} , then C\: = \: \max_{p(x_{1},x_{2})} \min \,{I(X_{1},X_{2};Y),I \,(X_{1};Y,Y_{1}|X_{2})} . 4)For a general relay channel, C \: \leq \: \max_{p(x_{1},x_{2})} \min \,{I \,(X_{1}, X_{2};Y),I(X_{1};Y,Y_{1}|X_{2}) . Superposition block Markov encoding is used to show achievability of C , and converses are established. The capacities of the Gaussian relay channel and certain discrete relay channels are evaluated. Finally, an achievable lower bound to the capacity of the general relay channel is established.

/pdf/capacity-theorems-for-the-relay-channel-5432o2a5q4.pdf

Capacity theorems for the relay channel

Let \{(X_{k}, Y_{k}) \}^{ \infty}_{k=1} be a sequence of independent drawings of a pair of dependent random variables X, Y . Let us say that X takes values in the finite set \cal X . It is desired to encode the sequence \{X_{k}\} in blocks of length n into a binary stream of rate R , which can in turn be decoded as a sequence \{ \hat{X}_{k} \} , where \hat{X}_{k} \in \hat{ \cal X} , the reproduction alphabet. The average distortion level is (1/n) \sum^{n}_{k=1} E[D(X_{k},\hat{X}_{k})] , where D(x,\hat{x}) \geq 0, x \in {\cal X}, \hat{x} \in \hat{ \cal X} , is a preassigned distortion measure. The special assumption made here is that the decoder has access to the side information \{Y_{k}\} . In this paper we determine the quantity R \ast (d) , defined as the infimum ofrates R such that (with \varepsilon > 0 arbitrarily small and with suitably large n )communication is possible in the above setting at an average distortion level (as defined above) not exceeding d + \varepsilon . The main result is that R \ast (d) = \inf [I(X;Z) - I(Y;Z)] , where the infimum is with respect to all auxiliary random variables Z (which take values in a finite set \cal Z ) that satisfy: i) Y,Z conditionally independent given X ; ii) there exists a function f: {\cal Y} \times {\cal Z} \rightarrow \hat{ \cal X} , such that E[D(X,f(Y,Z))] \leq d . Let R_{X | Y}(d) be the rate-distortion function which results when the encoder as well as the decoder has access to the side information \{ Y_{k} \} . In nearly all cases it is shown that when d > 0 then R \ast(d) > R_{X|Y} (d) , so that knowledge of the side information at the encoder permits transmission of the \{X_{k}\} at a given distortion level using a smaller transmission rate. This is in contrast to the situation treated by Slepian and Wolf [5] where, for arbitrarily accurate reproduction of \{X_{k}\} , i.e., d = \varepsilon for any \varepsilon >0 , knowledge of the side information at the encoder does not allow a reduction of the transmission rate.

/pdf/the-rate-distortion-function-for-source-coding-with-side-15w82p0ta1.pdf

The rate-distortion function for source coding with side information at the decoder

Consider a biased coin with probability of heads p. If p does not equal 0 or 1, there is not much that one can say with certainty about a single toss of the coin. However, for a sequence of N independent tosses, if one chooses N large enough one can make statements about the composition of this sequence which will be true with probability as close to 1 as desired.

The AEP Property of Random Sequences and Applications to Information Theory: Part I Basic Principles

A random multiple-access system which uses a collision resolution algorithm for accessing a common time-varying channel is considered. The channel is assumed to be in one of two states. In each state the channel is characterized by a general discrete memoryless channel, and the transitions between the two states are assumed to be Markovian. A set of sufficient conditions for the ergodicity (stability) of the system is established. As an example, the case when the Capetanakis tree algorithm operates with a time-varying noisy channel is examined. The stability of this system is analyzed and the throughput is evaluated. >

Random access systems with a time varying channel

: IN THE APPLICATION OF STATISTICAL DECISION THEORY TO THE RECOGNITION OF TWO-DIMENSIONAL PATTERNS IN NOISE, THE DECISION AS TO WHICH OF A SET OF PATTERNS IS PRESENT INVOLVES THE CALCULATIONS OF A LIKELIHOOD FUNCTION FOR EACH OF THE POSSIBLE SIGNALS In this paper, systems are developed for the calculation of these functions when the signal patterns are perturbed by multiplicative and additive noise The resulting realizations ARE SHOWN TO REDUCE TO TWO-DIMENSIONAL MATCHED FILTERS In the development, a useful orthogonal expansion of two-variable random processes is derived (Author)

On the recognition of signal patterns in noise

Methods and apparatuses for enhanced processing of received channels in a mobile communications system is described. Particularly, convolutionally encoded tail biting data in a mobile communications system is efficiently decoding by replicating the received encoded signal N times, where N equals a number of iterations. A Viterbi decoding algorithm is applied and a most likely survivor path is obtained. The ensuing decoding window is set as a fixed decoding window and placed at a mid-section of the most likely survivor path. Simulations have shown codeword accuracy to be comparable to MLSE with less complexity. A high degree of accuracy has been obtained for N=3.

Jack K. Wolf

Papers

The AEP Property of Random Sequences and Applications to Information Theory: Part I Basic Principles

Random access systems with a time varying channel

On the recognition of signal patterns in noise

Improved tail-biting convolutional decoding

Serieller viterbi-dekoder für unterschiedliche bitraten in cdma-systemen