Serially-Concatenated Low-Density Generator Matrix (SCLDGM) Codes for Transmission Over AWGN and Rayleigh Fading Channels

Abstract

Low Density Generator Matrix (LDGM) codes are a particular class of Low Density Parity Check (LDPC) codes with very low encoding complexity. Single LDGM codes present high error-floors, which can be substantially reduced with the serial concatenation of two LDGM (SCLDGM) codes. We propose a technique to obtain good SCLDGM codes using EXtrinsic Information Transfer (EXIT) functions in a novel way. Although the optimization is performed for AWGN channels with binary signaling, the resulting codes are also optimal for AWGN and perfectly-interleaved Rayleigh fading channels with non-binary signaling and perfect CSI at reception, provided that Gray mapping is utilized. Optimized regular and irregular SCLDGM codes outperform heuristically-designed LDGM codes existing in the literature, and have a performance similar to or better than that of Irregular Repeat Accumulate (IRA) codes.

Video over DSL with LDGM Codes for Interactive Applications

“…However, at least for a binary symmetric channel (BSC) it is has been analytically demonstrated [21] that concatenating two LDGM codes (applying one LDGM code after another) overcomes the onset of an error floor, while retaining LDGM's computational complexity, provided a belief-propagation (message-passing) decoding algorithm is employed. Later work [22] confirmed the findings of [21] for a Rayleigh channel and provides analysis on how best to configure LDGM codes.…”

Video over DSL with LDGM codes for interactive applications

“…However, at least for a binary symmetric channel (BSC) it is has been analytically demonstrated [17] that concatenating two LDGM codes (applying one LDGM code after another) overcomes the onset of an error floor, while retaining LDGM's computational complexity, provided a belief-propagation (message-passing) decoding algorithm is employed. Later work [18] confirmed the findings of [17] for a Rayleigh channel and provides analysis on how best to configure LDGM codes. In this paper, we simulate an erasure channel, which is not necessarily open to analysis in the way a BSC is but nevertheless occurs in practice after PHY-layer error recovery fails to recover a packet.…”

Myths and realities of rateless coding

“…Additional details are beyond the scope of this article, and so we refer the interested reader to [9] and the references in [2] for further details. 11 The 12 We remark that these deficiencies of LT codes are also shared by their fixed-rate counterparts; i.e., the non-systematic LDGM codes. These codes are known to exhibit high error floors (see for example [8] [8,12], among others.)…”

“…11 The 12 We remark that these deficiencies of LT codes are also shared by their fixed-rate counterparts; i.e., the non-systematic LDGM codes. These codes are known to exhibit high error floors (see for example [8] [8,12], among others.) be operating on a different code than the one used by the encoder at the transmitter.…”

“…Recent work focusing on these aspects include [7,10,11]. On the other hand, the first-mentioned difficulty 12 can be circumvented by serially concatenating the LT code with another code, and specific realizations of such schemes have already been mentioned earlier. For the sake of comparison, Fig.…”