Low-floor decoders for LDPC codes

Abstract

One of the most significant impediments to the use of LDPC codes in many communication and storage systems is the error-rate floor phenomenon associated with their iterative decoders. The error floor has been attributed to certain sub-graphs of an LDPC code's Tanner graph induced by so-called trapping sets. We show in this paper that once we identify the trapping sets of an LDPC code of interest, a sum-product algorithm (SPA) decoder can be custom-designed to yield floors that are orders of magnitude lower than the conventional SPA decoder. We present two classes of such decoders: a bi-mode syndrome-erasure decoder and three generalized-LDPC decoders. We demonstrate the effectiveness of these decoders for two codes, the rate-1/2 (2640,1320) Margulis code which is notorious for its floors and a rate-0.3 (640,192) quasi-cyclic code which has been devised for this study.

Irregular repeat-accumulate-like codes with improved error floor performance

“…Other methods such as interleaver design, modifying the sum-product algorithm and adding an outer code [14] are also applicable to GIRA codes and may further improve their error floor performance.…”

“…3 ), a constant combiner rate 2 (ρ = x), interleaver Π = [1,4,5,11,2,7,8,12,6,13,9,14,3,10]. (12)- (14), decoded with sumproduct decoding with a maximum of 1000 iterations.…”

A New High Performance Decoder for LDPC Codes

“…Figure 1 shows an error TS(4,2) of an LDPC code with a degree of bit nodes and check nodes (3,6) in which the LLR value of BN is computed by the sum of intrinsic information and extrinsic information from three related CN.…”

“…It was observed through simulations of many LDPC codes that, in the error floor region, a frame error event usually contains a single TS. The authors in [3,4] provide the method of combination of CN into Super Check Nodes (SCN), so that information from the error-free TS can correct the error TS. For example, the Margulis code introduced in [8] with 1320 TS and 1320 TS (Figure 1) are the most dominant TS in the error floor region of the Margulis code.…”

“…To reduce the influence of TS, in [3,4], the authors gave a solution which is to find the most dominant TS and propose the G-LDPC decoder (Generalized LDPC decoder), allowing improvement in decoding quality at the high E b /N 0 values (the error floor region). However, defining TS is complex and difficult to implement with great length LDPC codes.…”