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

Robust remote data checking

Remote data checking protocols, such as provable data possession (PDP) [1], allow clients that outsource data to untrusted servers to verify that the server continues to correctly store the data. Through the careful integration of forward error-correcting codes and remote data checking, a system can prove possession with arbitrarily high probability. We formalize this notion in the robust data possession guarantee. We distill the key performance and security require-ments for integrating forward error-correcting codes into PDP and describe an encoding scheme and file organization for robust data possession that meets these requirements. We give a detailed anal-ysis of this scheme and build a Monte-Carlo simulation to evaluate tradeoffs in reliability, space overhead, and performance. A prac-tical way to evaluate these tradeoffs is an essential input to sys-tem design, allowing the designer to choose the encoding and data checking protocol parameters that realize robust data possession

Flexible Verification of MPEG-4 Stream in Peer-to-Peer CDN

Abstract. The current packet based stream authentication schemes provide effective and efficient authentication over a group of packets transmitted on erasure channels. However, by fixing the packets in transmission, any packet manipulation will cause authentication failure. In p2p content delivery network where a proxy-in-the-middle is able to store, forward, transcode and transform the stream, previous schemes are simply unapplicable. To address the problem, we propose a flexible verification scheme that relies on special stream formats (i.e. Unequal Loss Protection ULP scheme [7]). We apply the so called Unequal Loss Verification ULV scheme into MPEG-4 framework. The encoding, packing, amortizing and verifying methods are elaborated in this paper. Our analysis shows that the scheme is secure and cost effective. The scheme is indeed content aware and ensures the verification rate intuitively reflecting a meaningful stream. Further on, we describe the general method of publishing and retrieving a stream in p2p CDN.