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Short survey about code on the graph by example of hardware friendlyquasi-cycle LDPC code. We consider two main properties of code: weightenumerator (well known from classic code theory) and Trapping setspseudocodewords weight spectrum (a subgraph in code graph's which becomereasone of decoding failure under Belief propagation). In paper we show fastmethods to measure first components of TS enumerator using EMD=ACE constrainsfor high girth codes on the graph using graph spectral classification method.This approach simplify solving trouble of agreed between minimal TS pseudocodeweight and code distance (which can be measure using knowledge of Authomorphismfor algebraic code design methods or measure using lattice reduction(LLL,BKZ)for random graph design methods). In the end of article author raise severalchallenge problems to improve Sparse and Dense parity-check codes decodingunder Belief propagation.

Some problems of Graph Based Codes for Belief Propagation decoding