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

On Comparing N-ary Systems

In high density magnetic recording, signals are often equalized to a partial response target of the form (1-D)(1+D)/sup n/ and then detected by a Viterbi detector using Euclidean distance. The authors use the ideas presented by L.C. Barbosa (1989) to estimate the performance degradation of several different equalizer targets for a tape channel, for a thin film disk channel, and for an ideal Lorentzian channel at a range of densities. The target 1+0.25D-0.75D/sup 2/-0.5D/sup 3/ is shown to outperform the EPR4 target over a large range of densities. It is shown that in the absence of coding there exists little opportunity for performance improvements beyond those found with this target. >

New equalizer targets for sampled magnetic recording systems

In high-density perpendicular magnetic recording channels, nonlinear transition shift (NLTS) is one of the distortions that can degrade the system performance. Write precompensation is a standard method used to combat the negative effect of NLTS. In this paper, we propose a modified pattern-dependent noise predictive (PDNP) detection algorithm for use on channels with electronics noise, transition jitter noise, and NLTS. We show that this detector can offer significant improvement in bit-error-rate (BER) compared to conventional Viterbi and PDNP detectors. Moreover, the system performance can be further improved by combining the new detector with a simple write precompensation scheme.

Mean-Adjusted Pattern-Dependent Noise Prediction for Perpendicular Recording Channels With Nonlinear Transition Shift

A technique for the construction of trellis codes that double the squared free Euclidean distance on the dicode (1-D) channel is presented. This technique uses periodic pruning and permutation of the trellis to ensure that a small detector path memory length is sufficient. Some high rate codes constructed using this technique are given.

Finite truncation depth trellis codes for the dicode channel

NAND flash memories are currently the most widely used flash memories. In a NAND flash memory, although a cell block consists of many pages, to rewrite one page, the whole block needs to be erased and reprogrammed. Block erasures determine the longevity and efficiency of flash memories. So when data is frequently reorganized, which can be characterized as a data movement process, how to minimize block erasures becomes an important challenge. In this paper, we show that coding can significantly reduce block erasures for data movement, and present several optimal or nearly optimal algorithms. While the sorting-based non-coding schemes require O(n log n) erasures to move data among n blocks, coding-based schemes use only O(n) erasures and also optimize the utilization of storage space.

/pdf/storage-coding-for-wear-leveling-in-flash-memories-xmadi555xg.pdf

Jack K. Wolf

Papers

On Comparing N-ary Systems

New equalizer targets for sampled magnetic recording systems

Mean-Adjusted Pattern-Dependent Noise Prediction for Perpendicular Recording Channels With Nonlinear Transition Shift

Finite truncation depth trellis codes for the dicode channel

Storage coding for wear leveling in flash memories