Hybrid LDPC codes and iterative decoding methods - i3s

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Hybrid LDPC codes and iterative decoding methods - i3s

2.5 Results 75

hybrid LDPC code number 1 is obtained by the method presented in section 2.3.3, when

setting the check node connection profile, all check nodes are in G(256), putting all the

redundancy variable nodes in G(256) and information variables in G(64). The connection

profiles for these two groups are then optimized with d vmax = 10. As already observed

in section 2.3.2, variable nodes in the highest order group are affected with as much high

connection degrees as possible, to balance the poor generalized component code. The

hybrid LDPC code number 2 is obtained by the method presented in section 2.3.3, when

setting the graph connections to be regular with constant variable degree d v = 2 and constant

check degree d c = 5. Although these thresholds are not better than the one of a

regular (d v = 2, d c = 4) GF(256) LDPC code, which is 0.5 dB [63], we can exhibit hybrid

LDPC distributions with better thresholds than the one of a regular (d v = 2, d c = 4)

GF(256) LDPC code, by allowing higher connection degrees. However, our purpose is

to point out the good finite length performance of hybrid LDPC codes, and that is why

we have focused on low connection degrees. For such low degrees, we are going to

see that hybrid LDPC codes have very good finite length performances, but they do not

approach the capacity as close as multi-edge type LDPC codes do. This is due to the

adopted detailed representation Π which cannot handle degree one variable nodes. However,

it would be an interesting perspective to switch from the detailed representation to a

multi-edge type representation for LDPC codes. This will certainly enable to get capacityapproaching

distributions with low connection degrees. Indeed, it has been shown in [30]

that introducing degree-1 variable nodes in non-binary LDPC codes makes the decoding

threshold getting closer to the theoretical limit. Modifying the representation of hybrid

LDPC code ensemble is therefore very interesting for future work. We only present in

table 2.2 the thresholds of the distributions which are used for the following finite length

simulations.

Figure 2.5 represents some frame error rate (FER) curves for different codes, all with

K = 1024 information bits and code rate one-half. Figure 2.5 shows the performance

curves of hybrid LDPC codes number 1 and 2 compared with Quasi-cyclic Tanner codes

from [1], irregular LDPC codes from [10], a GF(256) LDPC code, a protograph based

LDPC code from [26] and a multi-edge type LDPC code from [27] with code length

N = 2560 bits (K = 1280 information bits). This code has been specially design for low

error-floor. The graphs of the binary, non-binary and hybrid LDPC codes have been built

with the random PEG algorithm described in [51].

We see that the hybrid LDPC code number 1 has performance very close to the protograph

based LDPC code, while the hybrid LDPC code number 2 has better waterfall

performance than the protograph based LDPC code but higher error floor. Also, the hybrid

LDPC code number 2 has a worse waterfall region than a regular (dv = 2, dc = 4)

GF(256) LDPC code, but a better error floor. These two observations are clues to investigate

a finite length optimization of the hybrid LDPC code, in order to refine the structure

of the graph to achieve better error floor performance.

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