diff --git a/src/thesis/chapters/5_conclusion_and_outlook.tex b/src/thesis/chapters/5_conclusion_and_outlook.tex index bdfd6f4..3bf2d3e 100644 --- a/src/thesis/chapters/5_conclusion_and_outlook.tex +++ b/src/thesis/chapters/5_conclusion_and_outlook.tex @@ -72,10 +72,10 @@ performance difference was most pronounced at low numbers of maximum iterations. % Implications from experimental results These observations imply that the warm-start modification to -sliding-window decoding provides a universal improvement, as long as +sliding-window decoding provides a consistent improvement, as long as some care is taken with specifying the information to be passed to the subsequent window. -Not that this comes at no additional cost to the decoding complexity, +Note that this comes at no additional cost to the decoding complexity, since the only difference between warm- and cold-start sliding-window decoding is the initialization of the \ac{bp} messages. We expect similar behavior with other inner decoders that support diff --git a/src/thesis/chapters/abstract.tex b/src/thesis/chapters/abstract.tex new file mode 100644 index 0000000..b889141 --- /dev/null +++ b/src/thesis/chapters/abstract.tex @@ -0,0 +1,56 @@ +\chapter*{Abstract} + +% Current state of the art + +\Ac{qec} protects fragile quantum states against decoherence by +encoding logical information into a larger number of physical qubits. +Because the syndrome extraction circuitry is itself implemented on +noisy quantum hardware, practical \ac{qec} must be fault-tolerant, +accounting for errors introduced by the correction procedure itself. +Fault tolerance considerations and the syndrome extraction circuit +are captured by \acp{dem}, which provide a unified framework for passing +this information to the decoder. + +Accounting for fault tolerance substantially inflates the +decoding problem. +At the same time, \ac{qec} imposes strict latency constraints due to +the backlog problem, where syndrome data accumulates faster than it +can be decoded. +Together, these factors pose a serious challenge for practical decoders. +Sliding-window decoding addresses this challenge by exploiting the +repeated structure of the syndrome extraction circuitry, partitioning +the \ac{dem}'s check matrix into overlapping windows that can be +decoded sequentially. +This allows for an earlier start to the decoding process, before all +syndrome measurements have been completed, thereby lowering the latency. + +% Our work: Identify research gap + +In this thesis, we perform a review of the existing literature on +sliding-window decoding and draw an analogy to windowed +decoding for classical spatially-coupled low-density parity-check +(\acs{sc}-\acs{ldpc}) codes. +We recognize that in contrast to the latter, existing realizations +of sliding-window decoding for \ac{qec} discard the soft information +produced inside one window before moving to the next. + +% Our work: Warm-start + +% TODO: Quantify improvement. Also for conclusion +We propose warm-start sliding-window decoding, in which the +\ac{bp} messages on the edges crossing into the overlap region of the previous +window are reused to initialize the corresponding messages of the +next window. +The warm start is formulated first for plain \ac{bp} and then extended to +\ac{bp} with guided decimation (\acs{bpgd}). +For both plain min-sum \ac{bp} and \ac{bpgd} decoding, the warm-start +initialization provides a consistent improvement across all examined +parameter settings. +We attribute this to an effective increase in \ac{bp} iterations on +variable nodes in the overlap regions: each such VN is processed by +multiple consecutive windows, and warm-starting lets these +invocations accumulate iterations rather than restart from scratch. +Crucially, the warm-start modification incurs no additional +computational cost relative to cold-start decoding, as it differs +only in the initialization of the \ac{bp} messages. + diff --git a/src/thesis/main.tex b/src/thesis/main.tex index 812f297..e384a18 100644 --- a/src/thesis/main.tex +++ b/src/thesis/main.tex @@ -103,7 +103,7 @@ \maketitle \newpage -% \include{chapters/abstract} +\include{chapters/abstract} \cleardoublepage \pagenumbering{arabic}