Optimization with exit functions of GLDPC-Staircase codes for the BEC

Abstract

In a previous work we introduced the Generalized LDPCStaircase codes for the Binary Erasure Channel, based on LDPC-Staircase codes and Reed Solomon as component codes. In this paper we perform an asymptotic analysis, in terms of EXtrinsic Information Transfer functions and we derive an upper bound of the ML decoding threshold based on the area theorem. We use this analysis to study the impact of the internal LDPC-Staircase code rate on the performance, and show that the proposed Generalized LDPC-Staircase codes closely approach the channel capacity, with only a small number (E = 2, 3) of extra-repair symbols per check node.

Design of small rate, close to ideal, GLDPC-staircase AL-FEC codes for the erasure channel

“…These properties make GLDPC-Staircase codes an excellent AL-FEC solution for many situations that require erasure protection. If the current paper focuses on practical performance evaluations, in [16] we introduce an asymptotic analysis, in terms of EXtrinsic Information Transfer functions and we derive an upper bound of the ML decoding threshold based on the area theorem. Both papers nicely complement with one another.…”

“…Based on EXtrinsic Information Transfer (EXIT) functions, asymptotic analysis technique, the impact of this parameter on GLDPC codes performances using the upper bound on the ML decoding thresholdδ ML is studied. For more details on the asymptotic analysis of GLDPC-Staircase codes please refer to [16]. Table I provides, for each r G , as seen in Figure 3 that increasing the base code rate r L (i.e, increasing E) quickly increases the upper bound on the ML threshold until it reaches a stable value (i.e.…”

Good coupling between LDPC-staircase and Reed-Solomon for the design of GLDPC codes for the erasure channel

“…This upper bound is conjectured to be tight in a quite general settings, especially for codes defined by almost regular graphs (e.g. LDPC-Staircase codes) (see [20] for details). In this section, we apply and extend the same method to determine (IT +RS) and¯ ML for scheme B.…”

“…To derive the (IT +RS) and the upper bound of the ML threshold (¯ ML ≥ ML ) obtained by the scheme A, in [20] we extended the EXIT function method proposed in [19]. This upper bound is conjectured to be tight in a quite general settings, especially for codes defined by almost regular graphs (e.g.…”

“…In [20] we extend this method to the coding scheme A under (IT+RS) decoding and ML decoding. In case of (IT+RS) decoding, there is a tight relation between the EXIT curve and the density evolution (DE) equations of GLDPC Staircase codes under (IT+RS) decoding.…”