Noisy Network Coding with Partial DF

In this paper, we propose a noisy network coding integrated with partial decode-and-forward relaying for single-source multicast discrete memoryless networks (DMN's). Our coding scheme generalizes the partial-decode-compress-and-forward scheme (Theorem 7) by Cover and El Gamal. This is the first time the theorem is generalized for DMN's such that each relay performs both partial decode-and-forward and compress-and-forward simultaneously. Our coding scheme simultaneously generalizes both noisy network coding by Lim, Kim, El Gamal, and Chung and distributed decode-and-forward by Lim, Kim, and Kim. It is not trivial to combine the two schemes because of inherent incompatibility in their encoding and decoding strategies. We solve this problem by sending the same long message over multiple blocks at the source and at the same time by letting the source find the auxiliary covering indices that carry information about the message simultaneously over all blocks.Comment: 5 pages, 1 figure, to appear in Proc. IEEE ISIT 201

Cooperative Strategies for Simultaneous and Broadcast Relay Channels

Consider the \emph{simultaneous relay channel} (SRC) which consists of a set of relay channels where the source wishes to transmit common and private information to each of the destinations. This problem is recognized as being equivalent to that of sending common and private information to several destinations in presence of helper relays where each channel outcome becomes a branch of the \emph{broadcast relay channel} (BRC). Cooperative schemes and capacity region for a set with two memoryless relay channels are investigated. The proposed coding schemes, based on \emph{Decode-and-Forward} (DF) and \emph{Compress-and-Forward} (CF) must be capable of transmitting information simultaneously to all destinations in such set. Depending on the quality of source-to-relay and relay-to-destination channels, inner bounds on the capacity of the general BRC are derived. Three cases of particular interest are considered: cooperation is based on DF strategy for both users --referred to as DF-DF region--, cooperation is based on CF strategy for both users --referred to as CF-CF region--, and cooperation is based on DF strategy for one destination and CF for the other --referred to as DF-CF region--. These results can be seen as a generalization and hence unification of previous works. An outer-bound on the capacity of the general BRC is also derived. Capacity results are obtained for the specific cases of semi-degraded and degraded Gaussian simultaneous relay channels. Rates are evaluated for Gaussian models where the source must guarantee a minimum amount of information to both users while additional information is sent to each of them.Comment: 32 pages, 7 figures, To appear in IEEE Trans. on Information Theor

A Rate-Compatible Sphere-Packing Analysis of Feedback Coding with Limited Retransmissions

Recent work by Polyanskiy et al. and Chen et al. has excited new interest in using feedback to approach capacity with low latency. Polyanskiy showed that feedback identifying the first symbol at which decoding is successful allows capacity to be approached with surprisingly low latency. This paper uses Chen's rate-compatible sphere-packing (RCSP) analysis to study what happens when symbols must be transmitted in packets, as with a traditional hybrid ARQ system, and limited to relatively few (six or fewer) incremental transmissions. Numerical optimizations find the series of progressively growing cumulative block lengths that enable RCSP to approach capacity with the minimum possible latency. RCSP analysis shows that five incremental transmissions are sufficient to achieve 92% of capacity with an average block length of fewer than 101 symbols on the AWGN channel with SNR of 2.0 dB. The RCSP analysis provides a decoding error trajectory that specifies the decoding error rate for each cumulative block length. Though RCSP is an idealization, an example tail-biting convolutional code matches the RCSP decoding error trajectory and achieves 91% of capacity with an average block length of 102 symbols on the AWGN channel with SNR of 2.0 dB. We also show how RCSP analysis can be used in cases where packets have deadlines associated with them (leading to an outage probability).Comment: To be published at the 2012 IEEE International Symposium on Information Theory, Cambridge, MA, USA. Updated to incorporate reviewers' comments and add new figure

Iteratively Decoded Irregular Variable Length Coding and Sphere-Packing Modulation-Aided Differential Space-Time Spreading

In this paper we consider serially concatenated and iteratively decoded Irregular Variable Length Coding (IrVLC) combined with precoded Differential Space-Time Spreading (DSTS) aided multidimensional Sphere Packing (SP) modulation designed for near-capacity joint source and channel coding. The IrVLC scheme comprises a number of component Variable Length Coding (VLC) codebooks having different coding rates for the sake of encoding particular fractions of the input source symbol stream. The relative length of these source-stream fractions can be chosen with the aid of EXtrinsic Information Transfer (EXIT) charts in order to shape the EXIT curve of the IrVLC codec, so that an open EXIT chart tunnel may be created even at low Eb/N0 values that are close to the capacity bound of the channel. These schemes are shown to be capable of operating within 0.9 dB of the DSTS-SP channel’s capacity bound using an average interleaver length of 113, 100 bits and an effective bandwidth efficiency of 1 bit/s/Hz, assuming ideal Nyquist filtering. By contrast, the equivalent-rate regular VLC-based benchmarker scheme was found to be capable of operating at 1.4 dB from the capacity bound, which is about 1.56 times the corresponding discrepancy of the proposed IrVLC-aided scheme

A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes

In this paper, we study the impact of locality on the decoding of binary cyclic codes under two approaches, namely ordered statistics decoding (OSD) and trellis decoding. Given a binary cyclic code having locality or availability, we suitably modify the OSD to obtain gains in terms of the Signal-To-Noise ratio, for a given reliability and essentially the same level of decoder complexity. With regard to trellis decoding, we show that careful introduction of locality results in the creation of cyclic subcodes having lower maximum state complexity. We also present a simple upper-bounding technique on the state complexity profile, based on the zeros of the code. Finally, it is shown how the decoding speed can be significantly increased in the presence of locality, in the moderate-to-high SNR regime, by making use of a quick-look decoder that often returns the ML codeword.Comment: Extended version of a paper submitted to ISIT 201

Re-proving Channel Polarization Theorems: An Extremality and Robustness Analysis

The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that this class of codes, called polar codes, achieve the symmetric capacity --- the mutual information evaluated at the uniform input distribution ---of any stationary binary discrete memoryless channel with low complexity encoders and decoders requiring in the order of $O(N\log N)$ operations in the block-length $N$. This discovery settled the long standing open problem left by Shannon of finding low complexity codes achieving the channel capacity. Polar coding settled an open problem in information theory, yet opened plenty of challenging problems that need to be addressed. A significant part of this thesis is dedicated to advancing the knowledge about this technique in two directions. The first one provides a better understanding of polar coding by generalizing some of the existing results and discussing their implications, and the second one studies the robustness of the theory over communication models introducing various forms of uncertainty or variations into the probabilistic model of the channel.Comment: Preview of my PhD Thesis, EPFL, Lausanne, 2014. For the full version, see http://people.epfl.ch/mine.alsan/publication