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We present a new class of irregular low-density parity-check (LDPC) codes for moderate block lengths (up to a few thousand bits) that are well-suited for rate-compatible puncturing. The proposed codes show good performance under puncturing over a wide range of rates and are suitable for usage in incremental redundancy hybrid-automatic repeat request (ARQ) systems. In addition, these codes are linear-time encodable with simple shift-register circuits. For a block length of 1200 bits the codes outperform optimized irregular LDPC codes and extended irregular repeat-accumulate (eIRA) codes for all puncturing rates 0.6~0.9 (base code performance is almost the same) and are particularly good at high puncturing rates where good puncturing performance has been previously difficult to achieve. Index Terms--Efficient encoding, low-density parity-check (LDPC) code, puncturing, rate-compatible code.

We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, s_1-t_1 and s_2-t_2. The capacity region for this problem is not known; furthermore, the outer bounds on the region have a large number of inequalities which makes them hard to explicitly evaluate. In this work we consider a related problem. We assume that we only know certain minimum cut values for the network, e.g., mincut(S_i, T_j), where S_i ⊆ s_1, s_2 and T_j ⊆ t_1, t_2 for different subsets S_i and T_j. Based on these values, we propose an achievable rate region for this problem using linear network codes. Towards this end, we begin by defining a multicast region where both sources are multicast to both the terminals. Following this we enlarge the region by appropriately encoding the information at the source nodes, such that terminal t_i is only guaranteed to decode information from the intended source s_i, while decoding a linear function of the other source. The rate region depends upon the relationship of the different cut values in the network. [ABSTRACT FROM AUTHOR]

We present a new class of irregular low-density parity-check (LDPC) codes for moderate block lengths (up to a few thousand bits) that are well-suited for rate-compatible puncturing. The proposed codes show good performance under puncturing over a wide range of rates and are suitable for usage in incremental redundancy hybrid-automatic repeat request (ARQ) systems. In addition, these codes are linear-time encodable with simple shift-register circuits. For a block length of 1200 bits the codes outperform optimized irregular LDPC codes and extended irregular repeat-accumulate (eIRA) codes for all puncturing rates 0.6∼0.9 (base code performance is almost the same) and are particularly good at high puncturing rates where good puncturing performance has been previously difficult to achieve. [ABSTRACT FROM AUTHOR]