Channel Code Analysis and Design Using Multiple Variable-Length Codes in Parallel without Feedback

Design of Bilayer and Multi-layer LDPC Ensembles from Individual Degree Distributions

“…Relevant to our techniques is the work in [17] where (single-layer) LDPC codes are used for a BEC with an erasure rate that can take one of two values: full decoding is sought for the better channel, while for the worse channel some partial correction performance is specified. More related work includes non-asymptotic design of bilayer LDPC codes such as codes that enable decoder parallelism [13] and codes for incremental redundancy [14], [15], [16] (whose layer 2 is an LDGM code). Another indication of interest in bilayer/multi-layer codes is a parallel work on (non-LDPC) algebraic bilayer/multi-layer codes [18], [19], [20], [21].…”

“…Proof: See Appendix C. Remark 3: Although the right-hand side of (15) and the first argument in the min operator of ( 16) only have the variable y in them and thus may appear to only depend on layer 2, in fact their values depend on both layers through the function q(•). Moreover, it is not clear, apriori, which argument of the min operator of ( 16) will be smaller, and one must use the above procedure to calculate the values.…”

“…A bilayer LDPC code has a code graph in which the variable nodes are connected to two types of check nodes, allowing different connectivity to each type. There are several applications that motivate codes with bilayer structure: communication over the relay channel [7], decoder parallelization [13], multi-block coding [11], incremental redundancy [14], [15], [16], to name a few. Bilayer codes are a special case of MET codes that are defined at full generality in [6].…”