Binary-Tree Encoding for Uniform Binary Sources in Index Modulation Systems

Abstract

The problem of designing bit-to-pattern mappings and power allocation schemes for orthogonal frequency-division multiplexing (OFDM) systems that employ subcarrier index modulation (IM) is considered. We assume the binary source conveys a stream of independent, uniformly distributed bits to the pattern mapper, which introduces a constraint on the pattern transmission probability distribution that can be quantified using a binary tree formalism. Under this constraint, we undertake the task of maximizing the achievable rate subject to the availability of channel knowledge at the transmitter. The optimization variables are the pattern probability distribution (i.e., the bit-to-pattern mapping) and the transmit powers allocated to active subcarriers. To solve the problem, we first consider the relaxed problem where pattern probabilities are allowed to take any values in the interval [0, 1] subject to a sum probability constraint. We develop (approximately) optimal solutions to the relaxed problem by using new bounds and asymptotic results, and then use a novel heuristic algorithm to project the relaxed solution onto a point in the feasible set of the constrained problem. Numerical analysis shows that this approach is capable of achieving the maximum mutual information for the relaxed problem in low and high-SNR regimes and offers noticeable benefits in terms of achievable rate relative to a conventional OFDM-IM benchmark.

Enhanced Huffman Coded OFDM With Index Modulation

“…Here, we are only interested in the full binary tree because of its prefix-free property and instantaneous decodability [48]. For a full binary tree with S leaves, its architecture can be uniquely characterized by a set of depths S , among which the minimum and maximum depths are log 2 (S − 1) + 1 and S − 1, respectively [26]. Once the architecture of the Huffman tree used for Huffman encoding is given, the average encoding rate is fixed, which can be calculated by [24]…”

“…The approach to select unique tree architectures for an arbitrary number of SAPs has been detailed in [26]. On the other hand, the above observation does not imply that the Huffman tree with the largest depth is necessarily preferable.…”

“…• Different from the binary-tree coded OFDM-IM proposed in [26] that undertakes the task of optimizing the achievable rate subject to the availability of channel knowledge at the transmitter, we focus on the task of improving the error performance, which formulates a different optimization problem and employs a different optimization strategy.…”

Set Partition Modulation

“…At the receiver, the received signal is down converted and the cyclic prefix is then removed from each received baseband symbol vector before processing with an FFT. After employing 3 It is possible to utilize all set partitions by employing binary coding algorithms [15], [27].…”

“…Since all the schemes considered in this figure activate all subcarriers and the modulation order of the carried symbols on each subcarrier can be chosen to be the same, we ignore the modulation bits transmitted per subcarrier. Also, we do not restrict the codebook sizes to a power of two, since all the codewords in a codebook can be utilized by a binary coding technique such as Huffman coding regardless of the number of codewords [15], [27]. To reach the maximum number of index bits, DM-OFDM-IM modulates half of the subcarriers by one of the distinguishable constellations and the other half by the other constellation.…”