Ragnar Thobaben

Nested Polar Codes for Wiretap and Relay Channels

We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretappers channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.

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.

Polar Codes for Cooperative Relaying

We consider the symmetric discrete memoryless relay channel with orthogonal receiver components and show that polar codes are suitable for decode-and-forward and compress-and-forward relaying. In the first case we prove that polar codes are capacity achieving for the physically degraded relay channel; for stochastically degraded relay channels our construction provides an achievable rate. In the second case we construct sequences of polar codes that achieve the compress-and-forward rate by nesting polar codes for source compression into polar codes for channel coding. In both cases our constructions inherit most of the properties of polar codes. In particular, the encoding and decoding algorithms and the bound on the block error probability O(2-Nβ) which holds for any 0<;β<;1/2.

On distributed codes with noisy relays

In this paper, we address the design of distributed coding schemes for the 3-node relay channel with half-duplex constraint. We first discuss the general problem of optimally re-encoding noisy data at the relay and summarize recently proposed approximations. Based on an analysis of the extrinsic information transfer characteristics of the component codes we investigate the potential of ldquoweakrdquo turbo or LDPC codes which are employed by the source node in order to increase the reliability of the relay when decoding is not possible. The results show that we can indeed gain from the proposed code design.

Low-complexity iterative joint source-channel decoding for variable-length encoded Markov sources

In this paper, we present a novel packetized bit-level decoding algorithm for variable-length encoded Markov sources, which calculates reliability information for the decoded bits in the form of a posteriori probabilities (APPs). An interesting feature of the proposed approach is that symbol-based source statistics in the form of the transition probabilities of the Markov source are exploited as a priori information on a bit-level trellis. This method is especially well-suited for long input blocks, since in contrast to other symbol-based APP decoding approaches, the number of trellis states does not depend on the packet length. When additionally the variable-length encoded source data is protected by channel codes, an iterative source-channel decoding scheme can be obtained in the same way as for serially concatenated codes. Furthermore, based on an analysis of the iterative decoder via extrinsic information transfer charts, it can be shown that by using reversible variable-length codes with a free distance of two, in combination with rate-1 channel codes and residual source redundancy, a reliable transmission is possible even for highly corrupted channels. This justifies a new source-channel encoding technique where explicit redundancy for error protection is only added in the source encoder.

Sensor-Network-Aided Cognitive Radio: On the Optimal Receiver for Estimate-and-Forward Protocols Applied to the Relay Channel

Cognitive radio describes a promising concept for improving the utilization of radio spectrum. It allows secondary users to access licensed radio spectrum in an opportunistic fashion, given that the quality of service for primary users is maintained. In this scenario, the detection of unused radio spectrum is the main obstacle: it requires the recognition of low- power signals in a noisy environment. Therefore, we consider the case where cognitive users are supported by a wireless sensor network (WSN) providing beliefs on the event that the primary user is active. The beliefs provided by the WSN nodes are then combined by the cognitive radio in order to make a final decision. Due to limitations in complexity, power, and bandwidth, the WSN nodes apply the estimate-and-forward protocol to communicate their beliefs and to relay the beliefs of adjacent nodes. For the case where the WSN is subject to noisy communication links, we derive and analyze the optimal receiver which provides the cognitive radio with log-likelihood ratios for the estimated and forwarded hypotheses. The performance of the optimal receiver is compared to the performance of sub-optimal receivers.

Combining FEC and optimal soft-input source decoding for the reliable transmission of correlated variable-length encoded signals

We utilize both the implicit residual source correlation and the explicit redundancy from a forward error correction (FEC) scheme for the error protection of packetized variable-length encoded source indices. The implicit source correlation is exploited in a novel symbol-based soft-input a-posteriori probability (APP) decoder, which leads to an optimal decoding process in combination with a mean-squares or maximum a-posteriori probability estimation of the reconstructed source signal. When, additionally, the variable-length encoded source data is protected by channel codes, an iterative source-channel decoder can be obtained in the same way as for serially concatenated codes, where the outer constituent decoder is replaced by the proposed APP source decoder. Simulation results show that, by additionally considering the correlations between the variable-length encoded source indices, the error-correction performance can be highly increased.

Analysis of the expected error performance of cooperative wireless networks employing distributed space-time codes

In this paper, typical uplink scenarios in a cellular system are considered, where two cooperating mobile stations (serving, for example, as mobile relays) are transmitting the some information to a base station by using a distributed space-time coding scheme. Due to the distributed nature of the system, the transmitted signals are typically subject to different average path losses. For fixed distances between the mobile stations and the base station, the error performance of the distributed space-time coding scheme is determined analytically. Then, based on considerations concerning the spatial distribution of the mobile stations, analytical expressions for the distribution of the average path losses are derived and verified by means of simulations. These results are then used in order to compute the expected error performance of the system. It is shown that in most scenarios the average performance loss compared to a conventional multiple-antenna system with colocated antennas is less than 2 dB at a bit error rate of 10/sup -3/. The most significant performance losses occur for a large path-loss exponent.

Rate-Compatible LDPC Convolutional Codes Achieving the Capacity of the BEC

In this paper, we propose a new family of rate-compatible regular low-density parity-check (LDPC) convolutional codes. The construction is based on graph extension, i.e., the codes of lower rates are generated by successively extending the graph of the base code with the highest rate. Theoretically, the proposed rate-compatible family can cover all the rational rates from 0 to 1. In addition, the regularity of degree distributions simplifies the code optimization. We prove analytically that all the LDPC convolutional codes of different rates in the family are capable of achieving the capacity of the binary erasure channel (BEC). The analysis is extended to the general binary memoryless symmetric channel, for which a capacity-approaching performance can be achieved. Analytical thresholds and simulation results for finite check and variable node degrees are provided for both BECs and binary-input additive white Gaussian noise channels. The results confirm that the decoding thresholds of the rate-compatible codes approach the corresponding Shannon limits over both channels.