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

A method and apparatus for encoding and decoding QAM trellis modulated data. In the transmitter, a subset of bits of an input bit set are convolutionally encoded based upon a punctured convolutional code of a lower data rate to provide a set of coded symbols. The coded symbols and the uncoded bits of the input bit set are provided to a QAM modulator to provide a QAM modulation signal indicative of the values of coded symbols and the uncoded bits. In the receiver a QAM demodulator converts the received QAM signal to QAM signal space coordinates. A decoder employing the Viterbi algorithm is used to reconstruct a corrected estimate of the values of the coded data bits from the received signal coordinates. The corrected estimate of the values of the coded data bits are then used in conjunction with the received signal coordinates to provide corrected estimates of the values of the uncoded input bits.

Method and apparatus for encoding/decoding QAM trellis coded data

Statistical communication theory - A worker's view

In an orthogonal frequency division multiplexing (OFDM) system (10) which uses an outer Reed-Solomon encoder and interleaver (24) and an inner convolutional encoder (26), after the inner convolutional encoding the data bits are interleaved by an inner interleaver (28), and then grouped into symbols, each symbol having 'm' bits. After grouping, the symbols are mapped to a complex plane using quadrature amplitude modulation (QAM). Thus, bits, not symbols, are interleaved by the inner interleaver (28). A receiver (12) performs a soft decision regarding the value of each bit in each complex QAM symbol received.

Transmission of digital signals by orthogonal frequency division multiplexing

It is shown that under certain conditions, when convolutional codes with precoding are used in conjunction with a partial response channel, the number of decoder states in a maximum-likelihood decoder matched to both the code and channel is 1/2 of that predicted by J.K. Wolf and G. Ungerboeck (ibid., vol.COM-34, no.7, p.751-72, 1986). >

On saving decoder states for some trellis codes and partial response channels

A new iterative decoding scheme was developed for the cyclic redundancy check error correction code (CRCC), a concatenated error correction coding system. This simple iterative decoder achieves efficient cooperation between an outer Reed-Solomon error correction code (RS-ECC) decodes and a PRML trellis-detector. By using "error-free" decoded bit-information feedback from the outer RS-ECC decoder, the iterative scheme employs "state pinning" in the ML trellis-detector. This enables long error-events in the ML-decoded data to be corrected efficiently without adding extra coding redundancy and specific decoding complexity. The iterative scheme improves the correction capability of the outer RS-ECC coding by making use of a CRCC coding for specific correcting short error-events. Simulation shows that the iterative scheme achieves significant improvement in RS-ECC error-rate performance for a rate 16/17 quasi-MTR-coded Modified E/sup 2/PRML (ME/sup 2/PRML) channel in conjunction with CRCC coding.

Jack K. Wolf

Papers

Method and apparatus for encoding/decoding QAM trellis coded data

Statistical communication theory - A worker's view

Transmission of digital signals by orthogonal frequency division multiplexing

On saving decoder states for some trellis codes and partial response channels

Iterative decoding for concatenated error correction coding in PRML channel systems