Uniquely decodable multiple access source codes

The Slepian-Wolf bound raises interest in lossless code design for multiple access networks. Previous work treats instantaneous codes. We generalize the Sardinas and Patterson test and bound the achievable rate region for uniquely decodable codes. The Kraft inequality is generalised to produce the necessary conditions on the codeword lengths for uniquely decodable-side information source code

Fast Decoder for Overloaded Uniquely Decodable Synchronous Optical CDMA

In this paper, we propose a fast decoder algorithm for uniquely decodable (errorless) code sets for overloaded synchronous optical code-division multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code lengths, the proposed decoder has much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that the performance of the proposed decoder for a given BER requires only 1-2 dB higher signal-to-noise ratio (SNR) than the ML decoder.Comment: arXiv admin note: substantial text overlap with arXiv:1806.0395

Zero-error communication over adder MAC

Adder MAC is a simple noiseless multiple-access channel (MAC), where if users send messages $X_1,\ldots,X_h\in \{0,1\}^n$, then the receiver receives $Y = X_1+\cdots+X_h$ with addition over $\mathbb{Z}$. Communication over the noiseless adder MAC has been studied for more than fifty years. There are two models of particular interest: uniquely decodable code tuples, and $B_h$-codes. In spite of the similarities between these two models, lower bounds and upper bounds of the optimal sum rate of uniquely decodable code tuple asymptotically match as number of users goes to infinity, while there is a gap of factor two between lower bounds and upper bounds of the optimal rate of $B_h$-codes. The best currently known $B_h$-codes for $h\ge 3$ are constructed using random coding. In this work, we study variants of the random coding method and related problems, in hope of achieving $B_h$-codes with better rate. Our contribution include the following. (1) We prove that changing the underlying distribution used in random coding cannot improve the rate. (2) We determine the rate of a list-decoding version of $B_h$-codes achieved by the random coding method. (3) We study several related problems about R\'{e}nyi entropy.Comment: An updated version of author's master thesi

Network Codes for Real-Time Applications

We consider the scenario of broadcasting for real-time applications and loss recovery via instantly decodable network coding. Past work focused on minimizing the completion delay, which is not the right objective for real-time applications that have strict deadlines. In this work, we are interested in finding a code that is instantly decodable by the maximum number of users. First, we prove that this problem is NP-Hard in the general case. Then we consider the practical probabilistic scenario, where users have i.i.d. loss probability and the number of packets is linear or polynomial in the number of users. In this scenario, we provide a polynomial-time (in the number of users) algorithm that finds the optimal coded packet. The proposed algorithm is evaluated using both simulation and real network traces of a real-time Android application. Both results show that the proposed coding scheme significantly outperforms the state-of-the-art baselines: an optimal repetition code and a COPE-like greedy scheme.Comment: ToN 2013 Submission Versio

Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems

An algorithm for scalar quantizer design on discrete-alphabet sources is proposed. The proposed algorithm can be used to design fixed-rate and entropy-constrained conventional scalar quantizers, multiresolution scalar quantizers, multiple description scalar quantizers, and Wyner–Ziv scalar quantizers. The algorithm guarantees globally optimal solutions for conventional fixed-rate scalar quantizers and entropy-constrained scalar quantizers. For the other coding scenarios, the algorithm yields the best code among all codes that meet a given convexity constraint. In all cases, the algorithm run-time is polynomial in the size of the source alphabet. The algorithm derivation arises from a demonstration of the connection between scalar quantization, histogram segmentation, and the shortest path problem in a certain directed acyclic graph

Finite Field Multiple Access

In the past several decades, various multiple-access (MA) techniques have been developed and used. These MA techniques are carried out in complex-field domain to separate the outputs of the users. It becomes problematic to find new resources from the physical world. It is desirable to find new resources, physical or virtual, to confront the fast development of MA systems. In this paper, an algebraic virtual resource is proposed to support multiuser transmission. For binary transmission systems, the algebraic virtual resource is based on assigning each user an element pair (EP) from a finite field GF($p^m$). The output bit from each user is mapped into an element in its assigned EP, called the output symbol. For a downlink MA system, the output symbols from the users are jointly multiplexed into a unique symbol in the same field GF($p^m$) for further physical-layer transmission. The EPs assigned to the users are said to form a multiuser algebraic uniquely decodable (UD) code. Using EPs over a finite field, a network, a downlink, and an uplink orthogonal/non-orthogonal MA systems are proposed, which are called finite-field MA (FFMA) systems. Methods for constructing algebraic UD codes for FFMA systems are presented. An FFMA system can be designed in conjunction with the classical complex-field MA techniques to provide more flexibility and varieties.Comment: 32 pages, 10 figure

Lossless source coding for multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of jointly distributed information sequences {Xi}i=1∞ and {Yi}i=1∞ is drawn i.i.d. according to joint probability mass function (p.m.f.) p(x,y); the encoder for each source operates without knowledge of the other source; the decoder receives the encoded bit streams of both sources. The rate region for MASCs with arbitrarily small but non-zero error probabilities was studied by Slepian and Wolf. In this paper, we consider the properties of optimal truly lossless MASCs and apply our findings to practical truly lossless and near lossless code design