Serverless computing provides fine-grained resource elasticity for data analytics---a job can flexibly scale its resources for each stage, instead of sticking to a fixed pool of resources throughout its lifetime. Due to different data dependencies and different shuffling overheads caused by intra- and inter-server communication, the best degree of parallelism (DoP) for each stage varies based on runtime conditions.

An energy-efficient approach is presented for shaping a bit-interleaved low-density parity-check (LDPC) coded amplitude phase-shift keying (APSK) system. A subset of the interleaved bits output by a binary LDPC encoder are passed through a nonlinear shaping encoder whose output is more likely to be a zero than a one. The "shaping" bits are used to select from among a plurality of subconstellations, while the unshaped bits are used to select the symbol within the subconstellation. Because the shaping bits are biased, symbols from lower-energy subconstellations are selected more frequently than those from higher-energy subconstellations. An iterative decoder shares information among the LDPC decoder, APSK demapper, and shaping decoder. Information rates are computed for a discrete set of APSK ring radii and shaping bit probabilities, and the optimal combination of these parameters is identified for the additive white Gaussian noise (AWGN) channel. With the assistance of extrinsic-information transfer (EXIT) charts, the degree distributions of the LDPC code are optimized for use with the shaped APSK constellation. Simulation results show that the combination of shaping, degree-distribution optimization, and iterative decoding can achieve a gain in excess of 1 dB in AWGN at a rate of 3 bits/symbol compared with a system that does not use shaping, uses an unoptimized code from the DVB-S2 standard, and does not iterate between decoder and demodulator.

This paper considers a technique for shaping a turbo-coded amplitude-phase shift keying (APSK) constellation. After bit-interleaving, a subset of the bits output by a binary turbo encoder are passed through a nonlinear shaping encoder. The bits at the output of the shaping encoder are more likely to be a zero than a one. These "shaping'' bits are interleaved and used to select from among a plurality of subconstellations, while the unshaped bits are used to select the symbol within the subconstellation. Symbols from lower-energy subconstellations are selected more frequently than those from higher-energy subconstellations. Information rates are computed for a variety of APSK and shaping code parameters, in an effort to optimize these parameters. It is found that, in theory, shaping gains of slightly over 0.3 dB may be achieved with 16-APSK and 32-APSK in AWGN, while the gains in ergodic Rayleigh fading are slightly lower. Simulation results show the bit error performance of the constellation-shaping strategy with an actual turbo code. The BER results suggest that gains significantly beyond 0.3 dB may be possible in AWGN when an iterative decoder is used, presumably due to the additional coding gain of the shaping code.