10.1109/isit.2016.7541600
Kudekar, Shrinivas
Shrinivas
Kudekar
Kumar, Santhosh
Santhosh
Kumar
Mondelli, Marco
Marco
Mondelli0000-0002-3242-7020
Pfister, Henry D.
Henry D.
Pfister
Urbankez, Rudiger
Rudiger
Urbankez
Comparing the bit-MAP and block-MAP decoding thresholds of Reed-Muller codes on BMS channels
IEEE
2016
2019-07-31T06:36:16Z
2019-11-14T08:43:37Z
conference
/record/6733
/record/6733.json
1601.06048
The question whether RM codes are capacity-achieving is a long-standing open problem in coding theory that was recently answered in the affirmative for transmission over erasure channels [1], [2]. Remarkably, the proof does not rely on specific properties of RM codes, apart from their symmetry. Indeed, the main technical result consists in showing that any sequence of linear codes, with doubly-transitive permutation groups, achieves capacity on the memoryless erasure channel under bit-MAP decoding. Thus, a natural question is what happens under block-MAP decoding. In [1], [2], by exploiting further symmetries of the code, the bit-MAP threshold was shown to be sharp enough so that the block erasure probability also converges to 0. However, this technique relies heavily on the fact that the transmission is over an erasure channel. We present an alternative approach to strengthen results regarding the bit-MAP threshold to block-MAP thresholds. This approach is based on a careful analysis of the weight distribution of RM codes. In particular, the flavor of the main result is the following: assume that the bit-MAP error probability decays as N -δ , for some δ > 0. Then, the block-MAP error probability also converges to 0. This technique applies to transmission over any binary memoryless symmetric channel. Thus, it can be thought of as a first step in extending the proof that RM codes are capacity-achieving to the general case.