Computing sum of sources over an arbitrary multiple access channel

The problem of computing sum of sources over a multiple access channel (MAC) is considered. Building on the technique of linear computation coding (LCC) proposed by Nazer and Gastpar [2007], we employ the ensemble of nested coset codes to derive a new set of sufficient conditions for computing the sum of sources over an \textit{arbitrary} MAC. The optimality of nested coset codes [Padakandla, Pradhan 2011] enables this technique outperform LCC even for linear MAC with a structural match. Examples of nonadditive MAC for which the technique proposed herein outperforms separation and systematic based computation are also presented. Finally, this technique is enhanced by incorporating separation based strategy, leading to a new set of sufficient conditions for computing the sum over a MAC.Comment: Contains proof of the main theorem and a few minor corrections. Contents of this article have been accepted for presentation at ISIT201

Symbol-Level Noise-Guessing Decoding with Antenna Sorting for URLLC Massive MIMO

Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable latency. Only short codewords can eliminate the requirement for interleaving and reduce decoding latency. This paper suggests a coding and decoding method which, when combined with the high spectral efficiency of spatial multiplexing, can provide URLLC over a fading channel. Random linear coding and high-order modulation are used to transmit information over a massive multiple-input multiple-output (mMIMO) channel, followed by zero-forcing detection and guessing random additive noise decoding (GRAND) at a receiver. A variant of GRAND, called symbol-level GRAND, originally proposed for single-antenna systems that employ high-order modulation schemes, is generalized to spatial multiplexing. The paper studies the impact of the orthogonality defect of the underlying mMIMO lattice on symbol-level GRAND, and proposes to leverage side-information that comes from the mMIMO channel-state information and relates to the reliability of each receive antenna. This induces an antenna sorting step, which further reduces decoding complexity by over 80\% when compared to bit-level GRAND

Doubly-Irregular Repeat-Accumulate Codes over Integer Rings for Multi-user Communications

Structured codes based on lattices were shown to provide enlarged capacity for multi-user communication networks. In this paper, we study capacity-approaching irregular repeat accumulate (IRA) codes over integer rings $\mathbb{Z}_{2^{m}}$ for $2^m$-PAM signaling, $m=1,2,\cdots$. Such codes feature the property that the integer sum of $K$ codewords belongs to the extended codebook (or lattice) w.r.t. the base code. With it, \emph{% structured binning} can be utilized and the gains promised in lattice based network information theory can be materialized in practice. In designing IRA ring codes, we first analyze the effect of zero-divisors of integer ring on the iterative belief-propagation (BP) decoding, and show the invalidity of symmetric Gaussian approximation. Then we propose a doubly IRA (D-IRA) ring code structure, consisting of \emph{irregular multiplier distribution} and \emph{irregular node-degree distribution}, that can restore the symmetry and optimize the BP decoding threshold. For point-to-point AWGN channel with $$-PAM inputs, D-IRA ring codes perform as low as 0.29 dB to the capacity limits, outperforming existing bit-interleaved coded-modulation (BICM) and IRA modulation codes over GF($2^m$). We then proceed to design D-IRA ring codes for two important multi-user communication setups, namely compute-forward (CF) and dirty paper coding (DPC), with $2^m$-PAM signaling. With it, a physical-layer network coding scheme yields a gap to the CF limit by 0.24 dB, and a simple linear DPC scheme exhibits a gap to the capacity by 0.91 dB.Comment: 30 pages, 13 figures, submitted to IEEE Trans. Signal Processin

On the Properties of Error Patterns in the ConstantLee Weight Channel

The problem of scalar multiplication applied to vectors is considered in the Lee metric. Unlike in other metrics, the Lee weight of a vector may be increased or decreased by the product with a nonzero, nontrivial scalar. This problem is of particular interest for cryptographic applications, like for example Lee metric code-based cryptosystems, since an attacker may use scalar multiplication to reduce the Lee weight of the error vector and thus to reduce the complexity of the corresponding generic decoder. The scalar multiplication problem is analyzed in the asymptotic regime. Furthermore, the construction of a vector with constant Lee weight using integer partitions is analyzed and an efficient method for drawing vectors of constant Lee weight uniformly at random from the set of all such vectors is given

Algebraic approaches to distributed compression and network error correction

Algebraic codes have been studied for decades and have extensive applications in communication and storage systems. In this dissertation, we propose several novel algebraic approaches for distributed compression and network error protection problems. In the first part of this dissertation we propose the usage of Reed-Solomon codes for compression of two nonbinary sources. Reed-Solomon codes are easy to design and offer natural rate adaptivity. We compare their performance with multistage LDPC codes and show that algebraic soft-decision decoding of Reed-Solomon codes can be used effectively under certain correlation structures. As part of this work we have proposed a method that adapts list decoding for the problem of syndrome decoding. This in turn allows us to arrive at improved methods for the compression of multicast network coding vectors. When more than two correlated sources are present, we consider a correlation model given by a system of linear equations. We propose a transformation of correlation model and a way to determine proper decoding schedules. Our scheme allows us to exploit more correlations than those in the previous work and the simulation results confirm its better performance. In the second part of this dissertation we study the network protection problem in the presence of adversarial errors and failures. In particular, we consider the usage of network coding for the problem of simultaneous protection of multiple unicast connections, under certain restrictions on the network topology. The proposed scheme allows the sharing of protection resources among multiple unicast connections. Simulations show that our proposed scheme saves network resources by 4%-15% compared to the protection scheme based on simple repetition codes, especially when the number of primary paths is large or the costs for establishing primary paths are high

An Algebraic Framework for Multi-Terminal Communication.

We consider the problem of developing coding techniques and characterizing information-theoretic achievable rate regions for the following three multi-terminal communication channels. Firstly, we study an interference channel with three transmitter receiver pairs (3-IC). Secondly, we consider a broadcast channel with three receivers (3-BC), wherein three independent information streams are to be communicated to the three receivers. Thirdly, we consider a two user multiple access channel (MAC) with channel state information distributed at the transmitters (MAC-DSTx). The above channels are assumed discrete, memoryless and used without feedback. Current known coding technique for a general instance of these channels are based on independent unstructured codes. Recognizing the need for codes endowed with algebraic closure properties, we identify three ensembles of coset codes. We propose coding techniques based on these ensembles that exploit their algebraic closure property. We develop tools to characterize information-theoretic performance of the proposed coding techniques. These enable us derive achievable rate regions for a general instance of the above channels. The current known achievable rate regions can be enlarged by gluing together current known coding techniques and the ones proposed herein. Moreover, such an enlargement, as indicated below, is proven to be strict for certain instances. We identify additive and non-additive instances of 3-IC for which the derived achievable rate region is analytically proven to be strictly larger than current known largest. Moreover, for these channels, the proposed coding techniques based on coset codes is capacity achieving. We also identify a vector 3-BC for which the achievable rate region derived herein is analytically proven to be strictly larger than the current known largest. This vector 3-BC is the first known broadcast channel, for which superposition and binning of unstructured independent codes, proposed over three decades ago, can be strictly improved upon. We also identify non-additive and non-symmetric instances of MAC-DSTx for which the proposed coding technique is verified, through computation, to yield strictly larger achievable rate regions. Finally, we develop a coding technique based on nested coset codes to characterize a weaker set of sufficient conditions for the problem of computing sum of sources over a discrete memoryless MAC.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107264/1/arunpr_1.pd

Asymmetric Encryption for Wiretap Channels

Since the definition of the wiretap channel by Wyner in 1975, there has been much research to investigate the communication security of this channel. This thesis presents some further investigations into the wiretap channel which improve the reliability of the communication security. The main results include the construction of best known equivocation codes which leads to an increase in the ambiguity of the wiretap channel by using different techniques based on syndrome coding. Best known codes (BKC) have been investigated, and two new design models which includes an inner code and outer code have been implemented. It is shown that best results are obtained when the outer code employs a syndrome coding scheme based on the (23; 12; 7) binary Golay code and the inner code employs the McEliece cryptosystem technique based on BKC0s. Three techniques of construction of best known equivocation codes (BEqC) for syndrome coding scheme are presented. Firstly, a code design technique to produce new (BEqC) codes which have better secrecy than the best error correcting codes is presented. Code examples (some 50 codes) are given for the case where the number of parity bits of the code is equal to 15. Secondly, a new code design technique is presented, which is based on the production of a new (BEqC) by adding two best columns to the parity check matrix(H) of a good (BEqC), [n; k] code. The highest minimum Hamming distance of a linear code is an important parameter which indicates the capability of detecting and correcting errors by the code. In general, (BEqC) have a respectable minimum Hamming distance, but are sometimes not as good as the best known codes with the same code parameters. This interesting point led to the production of a new code design technique which produces a (BEqC) code with the highest minimum Hamming distance for syndrome coding which has better secrecy than the corresponding (BKC). As many as 207 new best known equivocation codes which have the highest minimum distance have been found so far using this design technique.Ministry of Higher Education and Scientific Research, Kurdistan Regional Government, Erbil-Ira