On The Design Of Physical Layer Rateless Codes

Codes that are capable of generating any number of encoded symbols from a given number of source symbols are called rateless codes. Luby transform (LT) codes are the first practical realization of rateless codes while Raptor codes are constructed by serially concatenating LT codes with high-rate outer low-density parity-check (LDPC) codes. Although these codes were originally developed for binary erasure channel (BEC), due to their rateless feature, they are being investigated and designed for their use in noisy channels. It is known that LT codes are the irregular non-systematic rateless counterpart of low-density generator-matrix (LDGM) codes. Therefore, the first part of our work is focused on LDGM codes and their serially concatenated scheme called serially concatenated LDGM (SCLDGM) codes. Though single LDGM codes are asymptotically bad codes, the SCLDGM codes are known to perform close to the Shannon limit. We first study the asymptotic behaviour of LDGM codes using a discretized density evolution method. We then show that the DDE method can be used in two-steps to provide the detailed asymptotic performance analysis of SCLDGM codes. We also provide the detailed error-floor analysis of both the LDGM and SCLDGM codes. We also prove a necessary condition for the successful decoding of such concatenated codes under sum-product (SP) decoding in binary input additive white Gaussian noise (BIAWGN) channels. Based on this necessary condition, we then develop a DDE-based optimization approach which can be used to optimize such concatenated codes in general. We present both the asymptotic performance and simulation results of our optimized SCLDGM codes that perform within 0.26 dB to the Shannon limit in BIAWGN channels. Secondly, we focus on the asymptotic analysis and optimization design of LT and Raptor codes over BIAWGN channels. We provide the exact asymptotic performance of LT codes using the DDE method. We apply the concept of the two-step DDE method to the Raptor codes and obtain their exact asymptotic performance in BIAWGN channels. We show that the existing Raptor codes using solely the same output degree distribution can perform within 0.4 dB to the Shannon limit for various realized code-rates. We then develop a DDE-based optimization technique to optimally design such physical layer Raptor codes. Our optimized Raptor codes are shown to perform within 0.2 dB to the Shannon limit for most of the realized code-rates. We also provide the asymptotic curves, decoding thresholds, and simulation results showing that our optimized Raptor codes outperform the existing Raptor codes in BIAWGN channels. Finally, we present the asymptotic analysis and optimization design of systematic version of these codes namely systematic LT and systematic Raptor codes as well

Raptor Codes in the Low SNR Regime

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BIAWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.Comment: Submitted to the IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1510.0772

Rateless Coding for Gaussian Channels

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.Comment: 18 page

Random Linear Network Coding for 5G Mobile Video Delivery

An exponential increase in mobile video delivery will continue with the demand for higher resolution, multi-view and large-scale multicast video services. Novel fifth generation (5G) 3GPP New Radio (NR) standard will bring a number of new opportunities for optimizing video delivery across both 5G core and radio access networks. One of the promising approaches for video quality adaptation, throughput enhancement and erasure protection is the use of packet-level random linear network coding (RLNC). In this review paper, we discuss the integration of RLNC into the 5G NR standard, building upon the ideas and opportunities identified in 4G LTE. We explicitly identify and discuss in detail novel 5G NR features that provide support for RLNC-based video delivery in 5G, thus pointing out to the promising avenues for future research.Comment: Invited paper for Special Issue "Network and Rateless Coding for Video Streaming" - MDPI Informatio