Jörg Kliewer

A Network Coding Approach to Cooperative Diversity

This paper proposes a network coding approach to cooperative diversity featuring the algebraic superposition of channel codes over a finite field. The scenario under consideration is one in which two ldquopartnersrdquo - node A and node B - cooperate in transmitting information to a single destination; each partner transmits both locally generated information and relayed information that originated at the other partner. A key observation is that node B already knows node As relayed information (because it originated at node B) and can exploit that knowledge when decoding node As local information. This leads to an encoding scheme in which each partner transmits the algebraic superposition of its local and relayed information, and the superimposed codeword is interpreted differently at the two receivers i.e., at the other partner and at the destination node, based on their different a priori knowledge. Decoding at the destination is then carried out by iterating between the codewords from the two partners. It is shown via simulation that the proposed scheme provides substantial coding gain over other cooperative diversity techniques, including those based on time multiplexing and signal (Euclidean space) superposition.

Memoryless relay strategies for two-way relay channels

We propose relaying strategies for uncoded two-way relay channels, where two terminals transmit simultaneously to each other with the help of a relay. In particular, we consider a memoryless system, where the signal transmitted by the relay is obtained by applying an instantaneous relay function to the previously received signal. For binary antipodal signaling, a class of so called absolute (abs)-based schemes is proposed in which the processing at the relay is solely based on the absolute value of the received signal. We analyze and optimize the symbol-error performance of existing and new abs-based and non-abs-based strategies under an average power constraint, including abs-based and non-abs-based versions of amplify and forward (AF), detect and forward (DF), and estimate and forward (EF). Additionally, we optimize the relay function via functional analysis such that the average probability of error is minimized at the high signal-to-noise ratio (SNR) regime. The optimized relay function is shown to be a Lambert W function parameterized on the noise power and the transmission energy. The optimized function behaves like abs-AF at low SNR and like abs-DF at high SNR, respectively; EF behaves similarly to the optimized function over the whole SNR range. We find the conditions under which each class of strategies is preferred. Finally, we show that all these results can also be generalized to higher order constellations.

The Design and Performance of Distributed LT Codes

This paper describes techniques to decompose LT codes (a class of rateless erasure-correcting codes) into distributed LT (DLT) codes. DLT codes can be used to independently encode data from multiple sources in a network in such a way that, when the DLT-encoded packets are combined at a common relay, the resulting bit stream (called a modified LT (MLT) code) has a degree distribution approximating that of an LT code, with simulations indicating comparable performance. In essence, DLT codes are designed so that the final stage of encoding for erasure correction can be carried out by a low-complexity relay that selectively xors the bit streams generated at each source and transmits the result to the sink. This paper presents results for two-source and four-source networks. It is shown that, when the relay-to-sink link is the bottleneck, the DLT/MLT approach can yield substantial performance benefits compared with a competing strategy wherein each of the sources uses its own independent LT encoder and the resulting bit streams are time-multiplexed through the relay.

Efficient Computation of EXIT Functions for Nonbinary Iterative Decoding

The calculation of nonbinary extrinsic information transfer charts for the iterative decoding of concatenated index-based codes is addressed. We show that the extrinsic information at the output of a constituent a posteriori probability decoder can be calculated with very low complexity, where expensive histogram measurements are not required any more. An example for turbo trellis-coded modulation demonstrates the capabilities of the proposed approach

Nested Codes with Multiple Interpretations

This paper proposes a new approach to channel code design for wireless network applications. The resulting nested codes can be decoded at different effective rates by different receivers-rates that depend on the prior knowledge possessed by each receiver; we say these codes have multiple interpretations. We have identified several applications in wireless networks where this property is useful. Specific nested code constructions as well as efficient soft and hard decision decoding algorithms are described. The concept of a nested code with multiple interpretations provides flexibility in the design of error protection schemes for multi-terminal wireless networks.

Iterative joint source-channel decoding of variable-length codes using residual source redundancy

We present a novel symbol-based soft-input a posteriori probability (APP) decoder for packetized variable-length encoded source indexes transmitted over wireless channels where the residual redundancy after source encoding is exploited for error protection. In combination with a mean-square or maximum APP estimation of the reconstructed source data, the whole decoding process is close to optimal. Furthermore, solutions for the proposed APP decoder with reduced complexity are discussed and compared to the near-optimal solution. When, in addition, channel codes are employed for protecting the variable-length encoded data, an iterative source-channel decoder can be obtained in the same way as for serially concatenated codes, where the proposed APP source decoder then represents one of the two constituent decoders. The simulation results show that this iterative decoding technique leads to substantial error protection for variable-length encoded correlated source signals, especially, when they are transmitted over highly corrupted channels.

Robust decoding of variable-length encoded Markov sources using a three-dimensional trellis

In this letter, we present an improved index-based a-posteriori probability (APP) decoding approach for the error-resilient transmission of packetized variable-length encoded Markov sources. The proposed algorithm is based on a novel two-dimensional (2D) state representation which leads to a three-dimensional trellis with unique state transitions. APP decoding on this trellis is realized by employing a 2D version of the BCJR algorithm where all available source statistics can be fully exploited in the source decoder. For an additional use of channel codes the proposed approach leads to an increased error-correction performance compared to a one-dimensional state representation.

Iterative Source-Channel Decoding With Markov Random Field Source Models

We propose a joint source-channel decoding approach for multidimensional correlated source signals. A Markov random field (MRF) source model is used which exemplarily considers the residual spatial correlations in an image signal after source encoding. Furthermore, the MRF parameters are selected via an analysis based on extrinsic information transfer charts. Due to the link between MRFs and the Gibbs distribution, the resulting soft-input soft-output (SISO) source decoder can be implemented with very low complexity. We prove that the inclusion of a high-rate block code after the quantization stage allows the MRF-based decoder to yield the maximum average extrinsic information. When channel codes are used for additional error protection the MRF-based SISO source decoder can be used as the outer constituent decoder in an iterative source-channel decoding scheme. Considering an example of a simple image transmission system we show that iterative decoding can be successfully employed for recovering the image data, especially when the channel is heavily corrupted

Space-Time Communication Protocols for N-Way Relay Networks

We address communication protocols for N-way relay networks with M antennas at the relay and a single antenna at the N source terminals. In particular, amplify-and-forward (AF), decode-and-forward (DF), and compress-and-forward (CF) strategies are extended to these networks, and in addition, two new relaying protocols, denoise-and-forward and estimate-and-forward, are proposed. In the first part of the paper, the performance of these schemes is analyzed in terms of the achievable rate region. Also, the optimal diversity-multiplexing tradeoff is derived for both AF and DF. The second part of the paper is devoted to practical space-time transmission strategies. Linear dispersion codes are used, which are optimized by maximizing the sum rate. For AF a diversity order of close to M can be achieved by using a specific space-time code construction.

On the Achievable Extrinsic Information of Inner Decoders in Serial Concatenation

In this paper we address the extrinsic information transfer functions of inner decoders for a serially concatenated coding scheme. For the case of an AWGN channel, we give a universal proof for the fact that only inner encoders yielding an infinite output weight for a weight-one input sequence, such as recursive convolutional encoders, lead to perfect extrinsic information at the output of the corresponding SISO decoder. As an example we consider bit-interleaved coded modulation with iterative demapping (BICM-ID) and insert an additional recursive precoder prior to the mapping operation. Simulation results show that the proposed system does not suffer from an error floor and thus significantly outperforms BICM-ID systems that solely use mappings as inner encodings, even when they are optimized