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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 consider the design and analysis of the efficiently-encodable rate-compatible (E²RC) irregular LDPC codes proposed in previous work. In this work we introduce semi-structured E²RC-like codes and protograph E²RC codes. EXIT chart based methods are developed for the design of semi-structured E²RC-like codes that allow us to determine near-optimal degree distributions for the systematic part of the code while taking into account the structure of the deterministic parity part, thus resolving one of the open issues in the original construction. We develop, a fast EXIT function computation method that does not rely on Monte-Carlo simulations and can be used in other scenarios as well. Our approach allows us to jointly optimize code performance across the range of rates under puncturing. We then consider protograph E²RC codes (that have a protograph representation) and propose rules for designing a family of rate-compatible punctured protographs with low thresholds. For both the semi-structured and protograph E²RC families we obtain codes whose gap to capacity is at most 0.3 dB across the range of rates when the maximum variable node degree is twenty. [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]