Mostafa El-Khamy

Iterative algebraic soft-decision list decoding of Reed-Solomon codes

In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft-decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity-check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation-based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation-based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of RS codes.

Fused DNN: A Deep Neural Network Fusion Approach to Fast and Robust Pedestrian Detection

We propose a deep neural network fusion architecture for fast and robust pedestrian detection. The proposed network fusion architecture allows for parallel processing of multiple networks for speed. A single shot deep convolutional network is trained as a object detector to generate all possible pedestrian candidates of different sizes and occlusions. This network outputs a large variety of pedestrian candidates to cover the majority of ground-truth pedestrians while also introducing a large number of false positives. Next, multiple deep neural networks are used in parallel for further refinement of these pedestrian candidates. We introduce a soft-rejection based network fusion method to fuse the soft metrics from all networks together to generate the final confidence scores. Our method performs better than existing state-of-the-arts, especially when detecting small-size and occluded pedestrians. Furthermore, we propose a method for integrating pixel-wise semantic segmentation network into the network fusion architecture as a reinforcement to the pedestrian detector. The approach outperforms state-of-the-art methods on most protocols on Caltech Pedestrian dataset, with significant boosts on several protocols. It is also faster than all other methods.

Performance Limits and Practical Decoding of Interleaved Reed-Solomon Polar Concatenated Codes

A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any ε > 0, and total frame length N, the parameters of the scheme can be set such that the frame error probability is less than 2-N1-ε, while the scheme is still capacity achieving. This improves upon 2-N0.5-ε, the frame error probability of Arikans polar codes. The proposed concatenated polar codes and Arikans polar codes are also compared for transmission over channels with erasure bursts. We provide a sufficient condition on the length of erasure burst which guarantees failure of the polar decoder. On the other hand, it is shown that the parameters of the concatenated polar code can be set in such a way that the capacity-achieving properties of polar codes are preserved. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity.

Performance of sphere decoding of block codes

The performance of sphere decoding of block codes over a variety of channels is investigated. We derive a tight bound on the performance of maximum likelihood decoding of linear codes on q-ary symmetric channels. We use this result to bound the performance of q-ary hard decision sphere decoders. We also derive a tight bound on the performance of soft decision sphere decoders on the AWGN channel for BPSK and M-PSK modulated block codes. The performance of soft decision sphere decoding of arbitrary finite lattices or block codes is also analyzed

Compound polar codes

A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar codes and then discuss our proposed scheme. Instead of encoding separately across the individual underlying channels, which requires multiple encoders and decoders, we take advantage of the recursive structure of polar codes to construct a unified scheme with a single encoder and decoder that can be used over the multi-channels. We prove that the scheme achieves the capacity over this multi-channel. Numerical analysis and simulation results for BICM channels at finite block lengths shows a considerable improvement in the probability of error comparing to a conventional separated scheme.

Polar Coding for Bit-Interleaved Coded Modulation

A polar coding scheme is proposed for reliable communication over channels with bit-interleaved coded modulation (BICM). In an ideal information-theoretic model, BICM schemes are modeled as a set of multiple binary-input channels that experience different reliabilities. This model is referred to as multichannel. The conventional scheme for encoding information over multi-channels is to encode separately across the individual constituent channels, which requires multiple encoders and decoders. As opposed to the conventional scheme, we take advantage of the recursive structure of polar codes to construct a unified compound polar code. The proposed scheme has a single encoder and decoder and can be used over multi-channels, in particular over channels with BICM. We prove that the scheme achieves the multi-channel capacity with the same error decay rate as in Arıkans polar codes. Furthermore, due to more levels of channel polarization, we obtain a better finite block length performance compared with the separated polarization scheme. This is confirmed through various simulations over the binary erasure channel and with transmissions over additive white Gaussian noise (AWGN) and fast fading channels with BICM and different modulation orders.

Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding

We consider the problem of polar coding for transmission over m-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a multiuser successive cancellation decoder is deployed at the receiver. The encoding is done separately across the users and is independent of the target achievable rate. For the code construction, the positions of information bits and frozen bits for each of the users are decided jointly. This is done by treating the polar transformations across all the m users as a single polar transformation with a certain polarization base. We characterize the resolution of achievable rates on the dominant face of the uniform rate region in terms of the number of users m and the length of the polarization base L. In particular, we prove that for any target rate on the dominant face, there exists an achievable rate, also on the dominant face, within the distance at most (m-1)√m/L from the target rate. We then prove that the proposed L MAC polar coding scheme achieves the whole uniform rate region with fine enough resolution by changing the decoding order in the multiuser successive cancellation decoder, as L and the code block length N grow large. The encoding and decoding complexities are O(N log N) and the asymptotic block error probability of O(2-N0.5-ϵ) is guaranteed. Examples of achievable rates for the 3-user multiple access channel are provided.

The partition weight enumerator of MDS codes and its applications

A closed form formula of the partition weight enumerator of maximum distance separable (MDS) codes is derived for an arbitrary number of partitions. Using this result, some properties of MDS codes are discussed. The results are extended for the average binary image of MDS codes in finite fields of characteristic two. As an application, we study the multiuser error probability of Reed Solomon codes

Joint space-time-view error concealment algorithms for 3D multi-view video

Efficiently compressing 3D multi-view video, while maintaining a high quality of received 3D video, is very challenging. Error Concealment (EC) algorithms have the advantage of improving the received video quality without modifications in the transmission rate or in the encoder hardware or software. To improve the quality of reconstructed 3D multi-view video, we propose different algorithms to conceal the erroneous and lost blocks of intra-coded and inter-coded frames by exploiting the spatial, temporal and inter-view correlations between frames and views. A hybrid of Space Domain Error Concealment (SDEC) and Time Domain Error Concealment (TDEC) is introduced for concealment of intra-frames errors. Three EC modes are introduced for inter-frames, which are Time Domain Error Concealment (TDEC), Inter-view Domain Error Concealment (IVDEC) and joint Time and Interview Domain Error Concealment (TIVDEC). Our simulation results show that the proposed algorithms can significantly improve the objective and subjective quality of reconstructed 3D multi-view video sequences.

Performance enhancements for algebraic soft decision decoding of Reed-Solomon codes

In an attempt to determine the ultimate capabilities of the Sudan-Guruswami-Sudan-Kotter-Vardy algebraic soft decision decoding algorithm for Reed-Solomon codes, we present a new method, based on the Chernoff bound, for constructing multiplicity matrices. In many cases, this technique predicts that the potential performance of ASD decoding of RS codes is significantly better than previously thought.