An explicit construction of concatenated codes for multiple access channels

Recently, a construction of polynomial-time decodable codes for discrete memoryless multiple access channels (MACs) has been proposed based on multi-level concatenated coding. This paper provides several refinements to concatenated codes for MACs. First, an explicit construction of inner codes is devised based on an ensemble of affine codes so that no search for good inner codes that achieve the capacity region is needed. Then a new decoding algorithm is proposed in which the inner decoding and the outer decoding alternate to improve a lower bound on the error exponent. It is shown that the proposed codes still arbitrarily approach every interior point of the capacity region for a given MAC with polynomial-time decoding complexity.