Georg Böcherer

Matching Dyadic Distributions to Channels

Many communication channels with discrete input have non-uniform capacity achieving probability mass functions (PMF). By parsing a stream of independent and equiprobable bits according to a full prefix-free code, a modulator can generate dyadic PMFs at the channel input. In this work, we show that for discrete memoryless channels and for memoryless discrete noiseless channels, searching for good dyadic input PMFs is equivalent to minimizing the Kullback-Leibler distance between a dyadic PMF and a weighted version of the capacity achieving PMF. We define a new algorithm called Geometric Huffman Coding (GHC) and prove that GHC finds the optimal dyadic PMF in O(m log m) steps where m is the number of input symbols of the considered channel. Furthermore, we prove that by generating dyadic PMFs of blocks of consecutive input symbols, GHC achieves capacity when the block length goes to infinity.

Operating LDPC codes with zero shaping gap

Unequal transition probabilities between input and output symbols, input power constraints, or input symbols of unequal durations can lead to non-uniform capacity achieving input distributions for communication channels. Using uniform input distributions reduces the achievable rate, which is called the shaping gap. Gallagers idea for reliable communication with zero shaping gap is to do encoding, matching, and jointly decoding and dematching. In this work, a scheme is proposed that consists in matching, encoding, decoding, and dematching. Only matching is channel specific whereas coding is not. Thus off-the-shelf LDPC codes can be applied. Analytical formulas for shaping and coding gap of the proposed scheme are derived and it is shown that the shaping gap can be made zero. Numerical results show that the proposed scheme allows to operate off-the-shelf LDPC codes with zero shaping gap and a coding gap that is unchanged compared to uniform transmission.

On spatial patterns of transmitter-receiver pairs that allow for interference alignment by delay

As a theoretical concept, and a means to understand the potential of interference alignment, in this paper we investigate possibilities to place n transmitter-receiver pairs in n — 1 dimensions such that the interference from unintended transmissions is aligned at each receiving node. By such an arrangement each link has half of the capacity available, at least in theory. Regular patterns of stations are considered. It is shown that placing transmitters “outside” a regular arrangement of receivers provides solutions in any dimension, while placing transmitters “opposite” to intended receivers only yields a solution in dimension one and two. Methodologically we borrow from the field of distance geometry.

Capacity Achieving Modulation for Fixed Constellations with Average Power Constraint

The capacity achieving probability mass function (PMF) of a finite signal constellation with an average power constraint is in most cases non-uniform. A common approach to generate non-uniform input PMFs is Huffman shaping, which consists of first approximating the capacity achieving PMF by a sampled Gaussian density and then to calculate the Huffman code of the sampled Gaussian density. The Huffman code is then used as a prefix-free modulation code. This approach showed good results in practice, can however lead to a significant gap to capacity. In this work, a method is proposed that efficiently constructs optimal prefix-free modulation codes for any finite signal constellation with average power constraint in additive noise. The proposed codes operate as close to capacity as desired. The major part of this work elaborates an analytical proof of this property. The proposed method is applied to 64-QAM in AWGN and numeric results are given, which show that, opposed to Huffman shaping, by using the proposed method, it is possible to operate very close to capacity over the whole range of parameters.

Cooperative protocols for random access networks

Cooperative communications have emerged as a significant concept to improve reliability and throughput in wireless systems. On the other hand, WLANs based on random access mechanism have become popular due to ease of deployment and low cost. Since cooperation introduces extra transmissions among the cooperating nodes and therefore increases the number of packet collisions, it is not clear whether there is any benefit from using physical layer cooperation under random access. In this paper, we develop new low complexity cooperative protocols for random access that outperform the conventional non cooperative scheme for a large range of signal-to-noise ratios.

Writing on the facade of RWTH ICT cubes: Cost constrained Geometric Huffman coding

In this work, a coding technique called cost constrained Geometric Huffman coding (ccGhc) is developed. ccGhc minimizes the Kullback-Leibler distance between a dyadic probability mass function (pmf) and a target pmf subject to an affine inequality constraint. An analytical proof is given that when ccGhc is applied to blocks of symbols, the optimum is asymptotically achieved when the blocklength goes to infinity. The derivation of ccGhc is motivated by the problem of encoding a text to a sequence of slats subject to architectural design criteria. For the considered architectural problem, for a blocklength of 3, the codes found by ccGhc match the design criteria. For communications channels with average cost constraints, ccGhc can be used to efficiently find prefix-free modulation codes that are provably capacity achieving.

Maximum entropy rate of Markov sources for systems with non-regular constraints

Using the concept of discrete noiseless channels, it was shown by Shannon in A Mathematical Theory of Communication that the ultimate performance of an encoder for a constrained system is limited by the combinatorial capacity of the system if the constraints define a regular language. In the present work, it is shown that this is not an inherent property of regularity but holds in general. To show this, constrained systems are described by generating functions and random walks on trees.

Short Huffman codes producing 1s half of the time

The design of the channel part of a digital communication system (e.g., error correction, modulation) is heavily based on the assumption that the data to be transmitted forms a fair bit stream. However, simple source encoders such as short Huffman codes generate bit streams that poorly match this assumption. As a result, the channel input distribution does not match the original design criteria. In this work, a simple method called half Huffman coding (HALFHC) is developed. HALFHC transforms a Huffman code into a source code whose output is more similar to a fair bit stream. This is achieved by permuting the codewords such that the frequency of 1s at the output is close to 0.5. The permutations are such that the optimality in terms of achieved compression ratio is preserved. HALFHC is applied in a practical example, and the resulting overall system performs better than when conventional Huffman coding is used.

Accelerating Resource Allocation for OFDMA Downlink with CNR Variation Over Users

This paper addresses the problem of resource alloca- tion for orthogonal frequency division multiple access (OFDMA) downlink that aims at minimizing the total transmission power under data transmission constraints. To accelerate this multiuser resource allocation with small performance loss, an efficient tech- nique is introduced that provides the power variation of single- user water-filling when the subcarrier assignment is changed. Based on this technique, an intelligent resource allocation method for OFDMA downlink is designed. First, a good starting point is determined by estimating the cardinality of the set of subcarriers that will be assigned to each user. Second, the convergence of the resource allocation is accelerated by reassigning those subcarriers first, which have the greatest channel-to-noise ratio (CNR) vari- ation over the users. Compared to previous works, simulations show that the presented method provides an improved balance between performance and computational complexity. I. INTRODUCTION Depending on channel characteristics, OFDMA can allocate power and rate optimally on subcarriers to take advantage of the spatial diversity among users in a fading environment. Concerning the problem of minimizing the total transmission power while satisfying individual transmission requirements of users, the method given in (1) provides the optimal solution and the methods proposed in (2), (3) achieve near-optimal per- formance, but they are computationally intensive and difficult to implement for a large number of users. Heuristic approaches with low complexity are suggested in (4)-(9) at the expense of performance loss in terms of allocated power. In this paper, we inherit the basic structure of the method suggested in (4), which consists of three consecutive algo- rithms. We introduce a new technique to efficiently update the transmission power after varying subcarrier assignments. The technique works best when subcarrier assignments are already close to good. Therefore, we suggest an intelligent initialization that chooses a good starting point by considering the estimated cardinalities of the sets of subcarriers that will be assigned to users. After that, the subcarriers are sorted according to their CNR variations over the users, such that subcarriers with higher CNR variations are reassigned first. In this way, our algorithm converges faster to the optimal solution. Simulations validate that little performance loss and much lower computing time is observed compared to SUSI This work has been supported by the UMIC Research Centre, RWTH Aachen University in Germany.

Throughput, bit-cost, network state information: Tradeoffs in cooperative CSMA protocols

In wireless local area networks, spatially varying channel conditions result in a severe performance discrepancy between different nodes in the uplink, depending on their position. Both throughput and energy expense are affected. Cooperative protocols were proposed to mitigate these discrepancies. However, additional network state information (NSI) from other nodes is needed to enable cooperation. The aim of this work is to assess how NSI and the degree of cooperation affect throughput and energy expenses. To this end, a CSMA protocol called fairMAC is defined, which allows to adjust the amount of NSI at the nodes and the degree of cooperation among the nodes in a distributed manner. By analyzing the data obtained by Monte Carlo simulations with varying protocol parameters for fairMAC, two fundamental tradeoffs are identified: First, more cooperation leads to higher throughput, but also increases energy expenses. Second, using more than one helper increases throughput and decreases energy expenses, however, more NSI has to be acquired by the nodes in the network. The obtained insights are used to increase the lifetime of a network. While full cooperation shortens the lifetime compared to no cooperation at all, lifetime can be increased by over 25% with partial cooperation.