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Design of Irregular Repeat Accumulate Codes for Finite Decoder Iterations

This paper deals with the design of non-systematic irregular repeat-accumulate codes that are optimised for a finite number of decoding iterations. In many cases of practical interest, the usual approach for sparse-graph codes, which aims to approach capacity (with arbitrarily many decoder iterations), may not be suitable. This is of particular importance for systems with complexity or delay constraints. In this paper, we provide a design methodology which constrains the number of decoder iterations, as well as other measures of implementation complexity. Our approach uses extrinsic information transfer analysis, and our main contribution is the formulation of code optimisation problems which directly incorporate the number of iterations into the constraints. We focus on the single user binary erasure channel and the two-user binary adder channel, where this transfer analysis is exact. Generalisation to other sparse graph codes and other channels (under usual approximations) is straightforward.