Channel coding may be viewed as the bestinformed and most potent component of cellular communication systems, which is used for correcting the transmission errors inflicted by noise, interference and fading. The powerful turbo code was selected to provide channel coding for Mobile Broad Band (MBB) data in the 3G UMTS and 4G LTE cellular systems. However, the 3GPP standardization group has recently debated whether it should be replaced by Low Density Parity Check (LDPC) or polar codes in 5G New Radio (NR), ultimately reaching the decision to adopt the LDPC code family for enhanced Mobile Broad Band (eMBB) data and polar codes for eMBB control. This paper summarises the factors that influenced this debate, with a particular focus on the Application Specific Integrated Circuit (ASIC) implementation of the decoders of these three codes. We show that the overall implementation complexity of turbo, LDPC and polar decoders depends on numerous other factors beyond their computational complexity. More specifically, we compare the throughput, error correction capability, flexibility, area efficiency and energy efficiency of ASIC implementations drawn from 110 papers and use the results for characterising the advantages and disadvantages of these three codes as well as for avoiding pitfalls and for providing design guidelines.

-A sufficient condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations is that the restricted isometry constant of the sensing matrix satisfies This result thus narrows the gap between the so far best known bound and the ultimate performance guaranteethat is conjectured by Dai and Milenkovic in 2009. The proposed approximate orthogonality condition is also exploited to derive less restricted sufficient conditions for signal reconstruction in several compressive sensing problems, including signal recovery via OMP in a noisy environment, compressive domain interference cancellation, and support identification via the subspace pursuit algorithm.

-A sufficient condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations is that the restricted isometry constant of the sensing matrix satisfies This result thus narrows the gap between the so far best known bound and the ultimate performance guaranteethat is conjectured by Dai and Milenkovic in 2009. The proposed approximate orthogonality condition is also exploited to derive less restricted sufficient conditions for signal reconstruction in several compressive sensing problems, including signal recovery via OMP in a noisy environment, compressive domain interference cancellation, and support identification via the subspace pursuit algorithm.

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