Constellation Shaping for Pragmatic Turbo-Coded Modulation With High Spectral Efficiency

Rate-adaptive constellation shaping for near-capacity achieving turbo coded BICM

“…2. The PMF for SN R ∈ [19; 21]dB is the one the authors used in [7]. Higher or lower SNR will have different optimal PMFs and dyadic GHC approximations.…”

“…However, the lack of any structure in the Huffman code results in a severe synchronization problem, especially when there is no error protection before it (as is the case if the VLC is used as an inner code, or in this case -a mapping function). In [7], the authors tackle this problem by appending ambiguous bits (taking a value of both '1' and a '0') to each bit sequence, after a constellation symbol is chosen. In this way the dyadic PMF is retained, but the label length is constant across symbols.…”

“…These criteria also ensure very good performance, when iterations between the decoder and the de-mapper are not allowed. In [7], the authors use a single 16PAM mapping function with label length of 6 bits, including the ambiguous bits. As shown in Section I, that PMF of the symbols is optimal only for a limited SNR range (Fig.…”

“…Dyadic PMFs are attractive because they can be achieved with binary data in a number of ways, e.g. with Variable Length Codes (VLC) [6] or a many-to-one strategy [7]. In [7] Raphaeli proposed a simple method for achieving a dyadic PMF, using the notion of pragmatic turbo codes [8].…”

“…with Variable Length Codes (VLC) [6] or a many-to-one strategy [7]. In [7] Raphaeli proposed a simple method for achieving a dyadic PMF, using the notion of pragmatic turbo codes [8]. However, the PMF is fixed and is designed for a certain SNR region, making it sub-optimal if a change in the spectral efficiency is required.…”