Ripple Design of LT Codes for BIAWGN Channels

Abstract

This paper presents a novel framework, which enables a design of rateless codes for binary input additive white Gaussian noise (BIAWGN) channels, using the ripple-based approach known from the works for the binary erasure channel (BEC). We reveal that several aspects of the analytical results from the BEC also hold in BIAWGN channels. The presented framework is applied in a code design example, which shows promising results compared to existing work. In particular it shows a great robustness towards variations in the signal-to-noise power ratio (SNR), contrary to existing codes. IEEE Transactions on CommunicationsThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-This paper presents a novel framework, which enables a design of rateless codes for binary input additive white Gaussian noise (BIAWGN) channels, using the ripple-based approach known from the works for the binary erasure channel (BEC). We reveal that several aspects of the analytical results from the BEC also hold in BIAWGN channels. The presented framework is applied in a code design example, which shows promising results compared to existing work. In particular it shows a great robustness towards variations in the signal-to-noise power ratio (SNR), contrary to existing codes.

Overlapped LT codes over the binary erasure channel: analysis and design

“…However, these have been proven to be hard problems. Instead, one can study the ripple behaviour (which is the number of degree-one encoded bits at each decoding step) of a given rateless code [20][21][22]. The dynamic behaviour of the decoding ripple is intimately related to the error performance, overhead, and complexity of code.…”

Expanding window fountain codes with intermediate feedback over BIAWGN channels

“…Previous studies on fountain codes have thus mainly been limited to erasure channels. Nevertheless, due to the advantages of simplicity, high performance, and flexibility of fountain codes compared to fixedrate FEC codes, there has been significant interest in the design of the former for noisy channels such as binary symmetric channels (BSCs) [6], fading channels [7,8], wireless relay channels [9], and binary input additive white Gaussian noise (BIAWGN) channels [10][11][12][13][14]. It is noteworthy that fountain codes are very applicable to other channels and can be used to approach channel capacity over various channels.…”

Joint Encoding and Decoding Optimization of LT Codes over Noise Channels

“…In [13], the influence of the degree distribution for decoding performance over noise channels is analyzed. In [14], a ripple-based degree design framework is presented to improve the performance of LT Codes over binary input additive white Gaussian noise (BIAWGN) channel. In [15], it was pointed out that speed up log-likelihood ratio (LLR) value transfer between the variable nodes (VNs) and the check nodes (CNs) can improve the decoding performance, and the corresponding degree optimization method is proposed.…”