Constellation shaping for IEEE 802.11

Abstract

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Prefix-Free Code Distribution Matching for Probabilistic Constellation Shaping

“…In [16], the multiset partitioning DM arXiv:1810.02411v2 [cs.IT] 3 Mar 2019 (MPDM) was proposed to enhance the degrading performance of CCDM in small blocks, by letting CCDM create different symbol distributions across multiple blocks that are averaged to the target distribution. For a small block length, typically below 100 symbols, there have been algorithmic approaches to implement an F2F DM, such as the shell mapping [17]- [19] and the enumerative sphere shaping [20]. The algorithmic approaches substantially reduced the complexity of indexing a point in a sphere, by divide and conquer [17]- [19] or dynamic programming [20], which is otherwise exponential in the dimension.…”

“…For a small block length, typically below 100 symbols, there have been algorithmic approaches to implement an F2F DM, such as the shell mapping [17]- [19] and the enumerative sphere shaping [20]. The algorithmic approaches substantially reduced the complexity of indexing a point in a sphere, by divide and conquer [17]- [19] or dynamic programming [20], which is otherwise exponential in the dimension. Nevertheless, their complexity is polynomial in the dimension, e.g., quadratic for the Algorithm 2 of [18], hence a large block length cannot be used.…”

“…:= (k − i=1 l(b (i) ))/R C2 is the number of required symbol slots in case we switch to C 2 at iteration + 1, respectively. Codebook C 1 is used for encoding at iteration if condition (20) is fulfilled, otherwise C 2 from iteration onwards. Notice that (20) can be evaluated only after seeing the incoming bits at iteration to obtain l(b ( ) ) and l(x ( ) ).…”

“…Codebook C 1 is used for encoding at iteration if condition (20) is fulfilled, otherwise C 2 from iteration onwards. Notice that (20) can be evaluated only after seeing the incoming bits at iteration to obtain l(b ( ) ) and l(x ( ) ). This makes unique decoding impossible, since, assuming that unique decoding was successfully performed until iteration − 1 such that l(b (i) ) and l(x (i) ) are known for all i = 1, .…”

Parallel-Amplitude Architecture and Subset Ranking for Fast Distribution Matching

“…The low-complexity DM of [11] generates two shaped output sequences for each binary input word and chooses the one with less average energy, which implicitly leads to a Gaussian-like distribution. In [12], an enumerative amplitude shaping method is proposed that is based on choosing those sequences in a trellis that have a certain maximum energy. The DM proposed in [13] compares different sequences generated by a mark ratio controller and selects the sequence that has desired properties.…”