Protograph E2RC Codes (pdf)
Fig. 1. Example of a starting protograph. The number next to an edge denotes the number of parallel edges between the variable and the check nodes.
The corresponding codes have a threshold of 3.27 dB which is 0.24 dB away from the theoretical limit.
Fig. 2. Two example mother code protographs for protograph E2RC codes constructed from the starting protograph in Fig. 1. Also shown is the gap to Shannon limit for the protograph at different puncturing rates 8/9 ~ 8/16.
It's clearly seen that for the protograph on the left, there is a uniformly good code performance at all code rates (constructed by following our construction rules). For the protograph on the right, it has an even lower threshold at some high code rates, but it comes at the expense of higher thresholds for the lower code rates.
Design of E2RC Codes Using EXIT Chart (pdf)
A new method for computing EXIT functions of the structured LDPC code components
EXIT charts have been an important tool for the design and analysis of LDPC codes. For standard irregular LDPC codes which are characterized by the degree distribution pair, the EXIT functions for the constituent code components involving all variable nodes and check nodes respectively have a closed form expression. For semi-structured LDPC codes, like the irregular-repeat-accumulate (IRA) codes and E2RC codes, the EXIT functions for the structured code components have to be computed with extra effort.
We proposed a new method for computing the EXIT functions of the structured LDPC code components, which is not a straightforward extension from the analysis of IRA codes as we explained in the paper (pdf). Bascially, we assign multiple edge types for the structured code component and compute its EXIT function by setting up and solving a system of equations which are totally dependent on the structure of the code component.
We use IRA codes as an example in our illustration on how our method can be applied in computing EXIT functions of structured LDPC code components.
Program download: Program 1 on computing EXIT
functions of the structured LDPC code components
Joint optimization of rate-compatible punctured LDPC codes and puncturing performance analysis
We proposed a new method for optimizing the performance of the rate-compatible punctured LDPC codes at multiple code rates simultaneously. Our codes achieve much uniformly good code performance compared with previous designs of rate-compatible punctured LDPC codes.
We use IRA codes as an example in our illustration on how to jointly optimize the code performance of IRA codes across all puncturing code rates.
Program download: Program
2 on jointly optimizing the code performance of IRA codes as a
rate-compatible punctured LDPC code