The encoding, decoding and performance analysis of concatenated partial unit memory (PUM) code structures for capacity approaching performance are investigated. PUM codes are known for their excellent distance properties and lower decoding complexity compared to equivalent multi-memory convolutional codes. Two capacity approaching concatenated structures are considered: turbo codes (TCs) and woven turbo codes (WTCs), both initially proposed with component convolutional codes. TCs consist of a number of parallel concatenated encoders. WTCs were originally proposed with outer warp, that is a number of outer encoders are parallel concatenated to one inner encoder. WTCs are also constructed with inner warp, i.e. one outer encoder is parallel concatenated to a number of inner encoders. An iterative max-log-maximum a posteriori decoding scheme is proposed for decoding PUM codes having multiple-input parallel branches in the trellis. The distance properties and bit error rate performance of the novel concatenated PUM codes are compared with known concatenated convolutional codes. It is observed that PUM structures, both TC and WTC with inner and outer warp, have better distance properties and hence improved performance over their equivalent convolutional counterparts. Performance as close as 1.25 dB from the Shannon limit is obtained for concatenated PUM structures with an interleaver size of only 4800 bits.