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

To optimize a high-density magnetic recording system, one needs to know the tradeoffs between various components of the system including the read/write transducers, the magnetic medium, and the read channel. In this paper, we consider a channel model characterized by three parameters: the replay pulse width T50, the transition jitter noise standard deviation sigmaJ, and the signal-to-electronic-noise ratio SNRWG. We utilize information-theoretic tools to determine the acceptable region for the channel parameters T50 and sigmaJ when optimal detection and linear coding techniques are used. This paper is an extension of a similar analysis for a system that utilized a minimum mean-squared error (MMSE) equalizer, a Viterbi detector, and a Reed-Solomon (RS) code. Our main conclusion is that there is a considerable potential gain to be achieved by using improved detection and coding schemes as compared with the present system

Design Curves and Information-Theoretic Limits for Perpendicular Recording Systems

In a communication system 10, a method and apparatus provide for decoding a sequence of turbo encoded data symbols. The channel nodes Rx, Ry and Rz are updated based on a received channel output, and the outgoing messages from symbol nodes (701, 707, 708) are initialized. The symbol nodes symbol nodes (701, 707, 708) are in communication with the channel nodes Rx, Ry and Rz. Updates of computational nodes C (704) and D (706) at different time instances are performed in accordance with a triggering schedule.

Turbo decoding method and apparatus for wireless communications

Flash memory is a non-volatile computer memory comprised of blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomplished only by erasing an entire block. Since block erasures are highly undesirable, coding schemes - known as floating codes or flash codes - have been designed in order to maximize the number of times that information stored in a flash memory can be written (and re-written) prior to incurring a block erasure. An (n,k,t)_q flash code C is a coding scheme for storing k information bits in n cells in such a way that any sequence of up to t writes (where a write is a transition 0 -> 1 or 1 -> 0 in any one of the k bits) can be accommodated without a block erasure. The total number of available level transitions in n cells is n(q-1), and the write deficiency of C, defined as \delta(C) = n(q-1) - t, is a measure of how close the code comes to perfectly utilizing all these transitions. For k > 6 and large n, the best previously known construction of flash codes achieves a write deficiency of O(qk^2). On the other hand, the best known lower bound on write deficiency is \Omega(qk). In this paper, we present a new construction of flash codes that approaches this lower bound to within a factor logarithmic in k. To this end, we first improve upon the so-called "indexed" flash codes, due to Jiang and Bruck, by eliminating the need for index cells in the Jiang-Bruck construction. Next, we further increase the number of writes by introducing a new multi-stage (recursive) indexing scheme. We then show that the write deficiency of the resulting flash codes is O(qk\log k) if q \geq \log_2k, and at most O(k\log^2 k) otherwise.

A Nearly Optimal Construction of Flash Codes

The bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence. This approach was previously introduced and applied to (d, k) constrained codes. Results show that the maximum average rate of the bit stuffing code achieves capacity when k=d+1 or k=/spl infin/, while it is suboptimal for all other (d, k) pairs. We propose a modification to the bit stuffing algorithm. We show analytically that the proposed algorithm achieves improved average rates over bit stuffing for most (d, k) constraints.

An improvement to the bit stuffing algorithm

A random multiple-access system which employs 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. >

Jack K. Wolf

Papers

Design Curves and Information-Theoretic Limits for Perpendicular Recording Systems

Turbo decoding method and apparatus for wireless communications

A Nearly Optimal Construction of Flash Codes

An improvement to the bit stuffing algorithm

Random-access systems with a time varying channel