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In the wireless local area network (WLAN) standard IEEE 802.11b, complementary code keying (CCK) modulation has been adopted for the high data rate transmission mode. In this paper, complexity reduction for block reduced-state sequence estimation (bRSSE), tailored for CCK transmission over frequency-selective channels, is considered. A trellis diagram for the chip phases of the codewords fully describes the CCK code properties. Subset trellises are derived from the full CCK trellis diagram based on set partitioning of the multidimensional CCK code set. The CCK subset trellises connect consecutive bRSSE states forming a compound trellis. The Viterbi algorithm (VA) with per-survivor processing is applied to the compound trellis to take the inter-chip interference into account. Inter-codeword interference is also accounted for by state-dependent decision feedback. The resulting scheme is denoted as bRSSE-pS and has a significantly lower complexity than bRSSE with bruteforce search over the entire CCK code set. By introducing a sphere constraint on the overall decoding trellis (SC-bRSSEpS), the complexity of bRSSE-pS can be further reduced. Omitting states in the CCK subset trellises that violate the sphere constraint, edges that emanate from such states can be pruned, and the average number of metric calculations per CCK trellis segment can be reduced. All presented schemes are also specialized to the case of a single bRSSE trellis state, resulting in block decision-feedback equalization (bDFE) algorithms with per-survivor processing and sphere decoding (bDFE-pS and SC-bDFE-pS, respectively). Simulation results show that the performance of bRSSE-pS (bDFE-pS) and SC-bRSSE-pS (SCbDFE-pS), respectively, is essentially equivalent to that of bRSSE (bDFE) with brute-force search over the entire CCK code set, while complexity is significantly reduced.