Olivier Pothier

Generalized low density (Tanner) codes

We build a class of pseudo-random error correcting codes, called generalized low density codes (GLD), from the intersection of two interleaved block codes. GLD code performance approaches the channel capacity limit and the GLD decoder is based on simple and fast SISO (soft input-soft output) decoders of smaller block codes. GLD codes are a special case of Tanner codes and a generalization of Gallagers LDPC codes. It is also proved by an ensemble performance argument that these codes are asymptotically good in the sense of the minimum distance criterion. The flexibility in selecting the parameters of GLD codes makes them suitable for small and large block length forward error correcting schemes.

Reduced complexity maximum a posteriori decoding of variable-length codes

Previously, joint source channel techniques mostly focused on systems using fixed-length coding, even though variable-length coding (VLC) is widely used, particularly in video coding. Typically, VLC bit streams are made channel-robust through packetization and standard forward-error correction (FEC). However, when the channel conditions are fairly mild, FEC can reveal itself bandwidth-inefficient. A variable-rate extension of joint source channel decoding could thus potentially replace FEC under mild conditions or, for noisier channels, could be used together with FEC to ameliorate the coding rate, extending in both cases the range of situations under which the bit stream is adequately protected. We propose two reduced-complexity VLC soft-input decoding techniques, as well as a comparison with existing algorithms. Experimental results of a new proposed VLC decoding algorithm show very good performance and low complexity.