Approximate Enumerative Sphere Shaping

Abstract

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Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

“…SR solves the CCDM indexing problem by representing a binary-alphabet sequence as a constant-order subset that determines the position of either binary symbol. For a given sorting, such as lexicographical, the rank of such a subset is found by “enumerating” all preceding sequences which is used for source coding in [ 96 , 97 ], and for shaping in [ 22 , 65 ]. This mapping from sequence to (binary) rank is called unranking in the combinatorics literature and acts as deshaping.…”

“…ESS is recently considered in PAS framework [ 48 , 60 , 61 , 62 , 63 ], as well as SM in [ 64 ]. Furthermore, low-complexity implementation ideas for both of these algorithms have been presented in [ 65 ].…”

Parallel-Amplitude Architecture and Subset Ranking for Fast Distribution Matching

“…2.4]). A similar approach has been applied by Schalkwijk [15] and Cover [16] for source coding, and recently been used in enumerative sphere shaping [21], [22]. We focus on highly parallel algorithms for subset ranking, with an application to CCDM, noting that the proposed approach can be used for any binary enumerative coding technique.…”

Partial Enumerative Sphere Shaping

“…Here m and p are called the mantissa and the exponent which are stored using n m and n p bits, respectively. The storage and computational complexities of this bounded-precision trellis computation and the corresponding indexing algorithms are L(N + 1)(n m + n p ) bits and (|A| − 1)(n m + n p ) bit oper./1-D, respectively [15].…”