Linear time encoding of cycle GF(2/sup P)/ codes through graph analysis

Low complexity soft demapping for non-binary LDPC codes

“…Non-binary channel codes (i.e., defined over high-order Galois Field (GF) q > 2) have been researched in the literature to achieve higher error protection than conventional binary codes for transmission over different noisy channels [1][2][3]. More recently, the European FP7 DAVINCI project [4] has explored the design of innovative non-binary Low Density Parity Check (LDPC) codes with tailored link level technologies over wireless fading channels, whilst aiming at small added complexity to conventional binary receivers.…”

Structure of non-binary regular ldpc cycle codes

“…. , e n }, where each vertex represents a constraint node corresponding to a row of H, and each edge represents a variable node corresponding to a column of H [8].…”

“…A linear time algorithm for solving these equations has been proposed in Lemma 4 of [8]. Note that solving these L 1 equations can be performed in parallel, thus encoding can be performed in parallel in linear time.…”

“…This provides a lot of flexibility in the implementation of efficient encoders, which is quite desirable especially when the codeword length is large. Note that the universal linear-time encoding algorithm presented in [8] can only work in a serial manner.…”

“…A universal linearcomplexity encoding algorithm for any cycle GF(q) code is This work is supported by the ONR grant N00014-07-1-0429 and the NSF grant ECCS-0725562. available in [8]. With the performance and implementation advantages, cycle GF(q) codes are very promising for practical applications.…”